Problem Set 2: Review

What is the appropriate statistical test? Report the null hypothesis. A pharmaceutical company would like to evaluate its newest weight-loss drug on women. Below are the weights of 12 women before and after having used the diet pill for three months. Using an alpha level of .05, test the hypothesis that the diet pill affects weight. Assume a normal distribution. before after 145 140 160 158 141 134 132 170 129 150 130 120 131 122 135 121 136 What is the appropriate statistical test? Report the null hypothesis. Report the alternative hypothesis. Find the critical value: Calculate the obtained statistic: Make a decision. What does your decision mean? Paired-samples t-test. The diet pill does NOT affect weight. The diet pill affects weight.

Two-tailed a=.05 11 df

What is the appropriate statistical test? Report the null hypothesis. A pharmaceutical company would like to evaluate its newest weight-loss drug on women. Below are the weights of 12 women before and after having used the diet pill for three months. Using an alpha level of .05, test the hypothesis that the diet pill affects weight. Assume a normal distribution. before after 145 140 160 158 141 134 132 170 129 150 130 120 131 122 135 121 136 D 5 2 -1 10 20 -11 30 8 14 4 What is the appropriate statistical test? Report the null hypothesis. Report the alternative hypothesis. Find the critical value: Calculate the obtained statistic: Make a decision. What does your decision mean? Paired-samples t-test. The diet pill does NOT affect weight. The diet pill affects weight. +/- 2.20

What is the appropriate statistical test? Report the null hypothesis. A pharmaceutical company would like to evaluate its newest weight-loss drug on women. Below are the weights of 12 women before and after having used the diet pill for three months. Using an alpha level of .05, test the hypothesis that the diet pill affects weight. Assume a normal distribution. before after 145 140 160 158 141 134 132 170 129 150 130 120 131 122 135 121 136 D 5 2 -1 10 20 -11 30 8 14 4 What is the appropriate statistical test? Report the null hypothesis. Report the alternative hypothesis. Find the critical value: Calculate the obtained statistic: Make a decision. What does your decision mean? Paired-samples t-test. The diet pill does NOT affect weight. The diet pill affects weight. +/- 2.20 Reject the null hypothesis. The diet pill affects weight.

_ x = 7.63 s = 3.50 𝑠 𝑥 = 3.5/√8 = 1.24 𝑡 𝑐𝑟𝑖𝑡 2 𝑡𝑎𝑖𝑙𝑒𝑑 = For the past 8 days I have been recording the time it takes a train to arrive at my local station. My data are below (in minutes). On a particular day, when I fear I may be running late to an important appointment, I have the option to take the train or I could spend money on a cab. I reach the station and wait for the train. Construct the 95% confidence interval of my wait estimate. Would you wait or take a cab at this point? Justify your answer using the confidence interval you calculated.   x = {5, 7, 12, 14, 4, 6, 6, 7} sample mean t critical value (look up in table) If 95% CI, use a=.05 If 99% CI, use a=.01 Remember, df = N-1 x = 7.63 _ Standard error s/sqrt(N) s = 3.50 𝑠 𝑥 = 3.5/√8 = 1.24 𝑡 𝑐𝑟𝑖𝑡 2 𝑡𝑎𝑖𝑙𝑒𝑑 =

Two-tailed a=.05 7 df

_ x = 7.63 s = 3.50 𝑠 𝑥 = 3.5/√8 = 1.24 𝑡 𝑐𝑟𝑖𝑡 2 𝑡𝑎𝑖𝑙𝑒𝑑 = +/- 2.37 For the past 8 days I have been recording the time it takes a train to arrive at my local station. My data are below (in minutes). On a particular day, when I fear I may be running late to an important appointment, I have the option to take the train or I could spend money on a cab. I reach the station and wait for the train. Construct the 95% confidence interval of my wait estimate. Would you wait or take a cab at this point? Justify your answer using the confidence interval you calculated.   x = {5, 7, 12, 14, 4, 6, 6, 7} sample mean t critical value (look up in table) If 95% CI, use a=.05 If 99% CI, use a=.01 Remember, df = N-1 x = 7.63 _ Standard error s/sqrt(N) s = 3.50 𝑠 𝑥 = 3.5/√8 = 1.24 𝑡 𝑐𝑟𝑖𝑡 2 𝑡𝑎𝑖𝑙𝑒𝑑 = +/- 2.37

For the past 8 days I have been recording the time it takes a train to arrive at my local station. My data are below (in minutes). On a particular day, when I fear I may be running late to an important appointment, I have the option to take the train or I could spend money on a cab. I reach the station and wait for the train. Construct the 95% confidence interval of my wait estimate. Would you wait or take a cab at this point? Justify your answer using the confidence interval you calculated.   x = {5, 7, 12, 14, 4, 6, 6, 7} x = 7.63 _ 7.63 + (2.37)(1.24) = 10.57 7.63 + (-2.37)(1.24) = 4.69 s = 3.50 𝑠 𝑥 = 3.5/√8 = 1.24 There is a 95% chance that the interval containing the true population mean is 4.69 to 10.57. 𝑡 𝑐𝑟𝑖𝑡 2 𝑡𝑎𝑖𝑙𝑒𝑑 = +/- 2.37

What is the appropriate statistical test? Report the null hypothesis. The Hershey company has been receiving complains about the number of almonds in their chocolate almond bars. Customers believe Hershey’s bars contain fewer almonds than they’ve previously contained because the company is trying to spend less money on their product. In a review of the company’s records from over the course of Hershey’s history, it was documented that each bar of candy contains a mean of 13 almonds with a standard deviation of 4 almonds. A sample of 49 of last month’s chocolate bars has been collected, and has a mean of 9 almonds. Test the hypothesis (a = .05) that Hershey’s has been skimping on almonds and thus there are fewer almonds in recent chocolate bars than in previous years. What is the appropriate statistical test? Report the null hypothesis. Report the alternative hypothesis. Find the critical value: Calculate the obtained statistic: Make a decision. What does your decision mean? z-test. 𝜇=13 Recent Hersheys do not have fewer almonds than usual. 𝜎=4 Recent Hersheys do have fewer almonds than usual. 𝑁=49 𝑥 =9 𝛼=.05 𝜇 𝑥 =13 𝜎 𝑥 =4/7 =.57

= 9−13 .57 = −7.02 What is the appropriate statistical test? The Hershey company has been receiving complains about the number of almonds in their chocolate almond bars. Customers believe Hershey’s bars contain fewer almonds than they’ve previously contained because the company is trying to spend less money on their product. In a review of the company’s records from over the course of Hershey’s history, it was documented that each bar of candy contains a mean of 13 almonds with a standard deviation of 4 almonds. A sample of 49 of last month’s chocolate bars has been collected, and has a mean of 9 almonds. Test the hypothesis (a = .05) that Hershey’s has been skimping on almonds and thus there are fewer almonds in recent chocolate bars than in previous years. What is the appropriate statistical test? Report the null hypothesis. Report the alternative hypothesis. Find the critical value: Calculate the obtained statistic: Make a decision. What does your decision mean? z-test. 𝜇=13 Recent Hersheys do not have fewer almonds than usual. 𝜎=4 Recent Hersheys do have fewer almonds than usual. -1.65 𝑁=49 𝑥 =9 𝛼=.05 𝑧 𝑜𝑏𝑡 = 𝑥 − 𝜇 𝑥 𝜎 𝑥 = 9−13 .57 = −7.02 𝜇 𝑥 =13 𝜎 𝑥 =4/7 =.57 Reject the null hypothesis. Recent Hersheys do have fewer almonds than usual.

Duration of Cold (days) Name Duration of Cold (days) Perle 3 Diane 5 Benjamin 8 Max 9 Rosie 12 Kamil Greg Briana 6 Stephen 4 Rita 11 Matt Sibel 7 Joanna 17 Stavros I believe that Zinc helps reduce the duration of a cold. On average, in the US, a cold lasts 7.5 days. I would like to ask a group of 14 friends to use Zinc for 1 year, and document the length of their colds (assuming they all become ill at least once that year). Using an alpha level of .01, test the hypothesis that Zinc reduces the duration of a cold, using the data below: What is the appropriate statistical test? Report the null hypothesis. Report the alternative hypothesis. Find the critical value: Calculate the obtained statistic: Make a decision. What does your decision mean? One-sample t-test 𝜇=7.5 𝑁=14 Zinc does not reduce the duration of a cold. 𝛼=.01 Zinc reduces the duration of a cold. 𝑥 =7.57 𝑠=3.74 𝜇 𝑥 =7.5 𝜎 𝑥 =3.74/√14 =1

one-tailed a=.01 13 df

Duration of Cold (days) Name Duration of Cold (days) Perle 3 Diane 5 Benjamin 8 Max 9 Rosie 12 Kamil Greg Briana 6 Stephen 4 Rita 11 Matt Sibel 7 Joanna 17 Stavros I believe that Zinc helps reduce the duration of a cold. On average, in the US, a cold lasts 7.5 days. I would like to ask a group of 14 friends to use Zinc for 1 year, and document the length of their colds (assuming they all become ill at least once that year). Using an alpha level of .01, test the hypothesis that Zinc reduces the duration of a cold, using the data below: What is the appropriate statistical test? Report the null hypothesis. Report the alternative hypothesis. Find the critical value: Calculate the obtained statistic: Make a decision. What does your decision mean? One-sample t-test 𝜇=7.5 𝑁=14 Zinc does not reduce the duration of a cold. 𝛼=.01 Zinc reduces the duration of a cold. -2.65 𝑥 =7.57 𝑠=3.74 𝑡 𝑜𝑏𝑡 = 𝑥 − 𝜇 𝑥 𝜎 𝑥 = 7.57−7.5 1 = .07 𝜇 𝑥 =7.5 𝜎 𝑥 =3.74/√14 =1 Retain the null hypothesis. Zinc does not the duration of a cold.

Fair coin: Heads = 50%, Tails = 50% Assume I toss a fair coin exactly 17 times. Find the probability of the following outcomes: a. 4 tails = .0182 b. 17 tails = .0000 c. 5 heads = .0472 d. 17 heads = .0000 e. 13 or more tails = .0245 f. 5 or less tails = .0717

If Heads = 45%, Tails = 55% a. 4 tails =.0068 b. 17 tails = .0000 Now assume I toss an unfair coin (45% baseline probability for Heads) 17 times as well:   a. 4 tails =.0068  b. 17 tails = .0000  c. 5 heads = .0875  d. 17 heads = .0000  e. 13 or more tails = .0595  f. 5 or less tails = .0302  If Heads = 45%, Tails = 55%

a. Reaching in once and pulling out a red writing utensil? I walk into the Psych department and notice that there is a box of pens and pencils being given away for free. They are all Brooklyn College-brand pens and pencils so they all have the same size and shape—the only way to tell whether it’s a pen or a pencil is to write with it. It turns out, however, that they do vary in color. The breakdown in the box is as follows: 4 red pens 2 red pencils 2 blue pens 8 blue pencils 9 black pens Evaluate the probability for each of the following, assuming you are starting with a fresh box for each question. (assume WITHOUT replacement for multiple reaches): Please report all probabilities to FOUR decimal places. a. Reaching in once and pulling out a red writing utensil? 6/25 = .2400 b. Reaching in once and pulling out a blue pen? 2/25 = .0800 c. Reaching in twice and pulling out a red utensil followed by a blue utensil? (6/25) (10/24) = .1000 d. Reaching in three times and pulling out three blue pencils in a row? (8/25) (7/24) (6/23) = .0243 e. Reaching in 6 times and pulling out the following sequence: Red pen, blue pencil, blue pencil, red pen, blue pencil, blue pencil (4/25) (8/24) (7/23) (3/22) (6/21) (5/20) = .0002

f. Reaching in once and pulling out either a red or a blue pen? I walk into the Psych department and notice that there is a box of pens and pencils being given away for free. They are all Brooklyn College-brand pens and pencils so they all have the same size and shape—the only way to tell whether it’s a pen or a pencil is to write with it. It turns out, however, that they do vary in color. The breakdown in the box is as follows: 4 red pens 2 red pencils 2 blue pens 8 blue pencils 9 black pens Evaluate the probability for each of the following, assuming you are starting with a fresh box for each question. (assume WITHOUT replacement for multiple reaches): Please report all probabilities to FOUR decimal places. f. Reaching in once and pulling out either a red or a blue pen? (4/25) + (2/25) = .2400 g. Reaching in once and pulling out either a black pen, a blue pencil, or a red utensil? (9/25) + (8/25) + (6/25) = .9200 h. Reaching in twice and pulling out either a red utensil or a pen? (6/25) + (15/25) - (4/25) = .6800 i. Reaching twice and pulling first a black pen and then either a blue utensil or a pencil? Black pen AND (either a blue utensil OR a pencil) = (9/25) ( ) (10/24) + (10/24) - (8/24) = .1800

What is the appropriate statistical test? Report the null hypothesis. Below are pupil sizes from two samples: 8 men and 8 women (measured in millimeters). Test the hypothesis that there is a difference in pupil sizes between males and females, using an alpha level of .01. What is the appropriate statistical test? Report the null hypothesis. Report the alternative hypothesis. Find the critical value: Calculate the obtained statistic: Make a decision. What does your decision mean? Independent-samples t-test males females 7.7 8.9 7.5 8.7 6.9 9.0 7.8 8.8 7.9 4.5 There is not a diff in pupil size between males and females. There is a diff in pupil size between males and females.

two-tailed a=.01 14 df

Below are pupil sizes from two samples: 8 men and 8 women (measured in millimeters). Test the hypothesis that there is a difference in pupil sizes between males and females, using an alpha level of .01. What is the appropriate statistical test? Report the null hypothesis. Report the alternative hypothesis. Find the critical value: Calculate the obtained statistic: Make a decision. What does your decision mean? Independent-samples t-test males females 7.7 8.9 7.5 8.7 6.9 9.0 7.8 8.8 7.9 4.5 There is not a diff in pupil size between males and females. There is a diff in pupil size between males and females. +/- 2.977 𝑡 𝑜𝑏𝑡 = 𝑥 1 − 𝑥 2 𝑠 𝑥1−𝑥2 = 7.06−8.76 𝑥 = 7.06 8.76

Below are pupil sizes from two samples: 8 men and 8 women (measured in millimeters). Test the hypothesis that there is a difference in pupil sizes between males and females, using an alpha level of .01. 𝑠 𝑥1−𝑥2 = 𝑆𝑆 1 + 𝑆𝑆 2 𝑛 1 + 𝑛 2 −2 1 𝑛 1 + 1 𝑛 2 What is the appropriate statistical test? Report the null hypothesis. Report the alternative hypothesis. Find the critical value: Calculate the obtained statistic: Make a decision. What does your decision mean? Independent-samples t-test males females 7.7 8.9 7.5 8.7 6.9 9.0 7.8 8.8 7.9 4.5 There is not a diff in pupil size between males and females. There is a diff in pupil size between males and females. +/- 2.977 𝑡 𝑜𝑏𝑡 = 𝑥 1 − 𝑥 2 𝑠 𝑥1−𝑥2 = 7.06−8.76 𝑥 = 7.06 8.76

How to find the Sum of Squares (SS) for each group: males females 7.7 8.9 7.5 8.7 6.9 9.0 7.8 8.8 7.9 4.5

How to find the Sum of Squares (SS) for each group: males females 7.7 8.9 7.5 8.7 6.9 9.0 7.8 8.8 7.9 4.5

How to find the Sum of Squares (SS) for each group: males males2 females females2 7.7 8.9 7.5 8.7 6.9 9.0 7.8 8.8 7.9 4.5

How to find the Sum of Squares (SS) for each group: males males2 females females2 7.7 59.29 8.9 79.21 7.5 56.25 8.7 75.69 6.9 47.61 9.0 81 7.8 60.84 8.8 77.44 7.9 62.41 4.5 20.25 𝑆𝑆 𝑚𝑎𝑙𝑒𝑠 = 𝑥 2 − 𝑥 2 𝑁 𝑆𝑆 𝑚𝑎𝑙𝑒𝑠 = 407.39 - 56.5 2 8 𝑆𝑆 𝑚𝑎𝑙𝑒𝑠 = 407.39 - 3192.25 8 𝑆𝑆 𝑚𝑎𝑙𝑒𝑠 = 407.39 - 399.03 S 56.5 407.39 70.1 615.19 𝑆𝑆 𝑚𝑎𝑙𝑒𝑠 = 8.36

How to find the Sum of Squares (SS) for each group: males males2 females females2 7.7 59.29 8.9 79.21 7.5 56.25 8.7 75.69 6.9 47.61 9.0 81 7.8 60.84 8.8 77.44 7.9 62.41 4.5 20.25 𝑆𝑆 𝑓𝑒𝑚𝑎𝑙𝑒𝑠 = 𝑥 2 − 𝑥 2 𝑁 𝑆𝑆 𝑓𝑒𝑚𝑎𝑙𝑒𝑠 = 615.19 - 70.1 2 8 𝑆𝑆 𝑓𝑒𝑚𝑎𝑙𝑒𝑠 = 615.19 - 4914.01 8 𝑆𝑆 𝑓𝑒𝑚𝑎𝑙𝑒𝑠 = 615.19 - 614.25 S 56.5 407.39 70.1 615.19 𝑆𝑆 𝑓𝑒𝑚𝑎𝑙𝑒𝑠 = .94

Below are pupil sizes from two samples: 8 men and 8 women (measured in millimeters). Test the hypothesis that there is a difference in pupil sizes between males and females, using an alpha level of .01. What is the appropriate statistical test? Report the null hypothesis. Report the alternative hypothesis. Find the critical value: Calculate the obtained statistic: Make a decision. What does your decision mean? Independent-samples t-test males females 7.7 8.9 7.5 8.7 6.9 9.0 7.8 8.8 7.9 4.5 There is not a diff in pupil size between males and females. There is a diff in pupil size between male and females. +/- 2.977 𝑡 𝑜𝑏𝑡 = 𝑥 1 − 𝑥 2 𝑠 𝑥1−𝑥2 = 7.06−8.76 SS 8.36 .94 N 8

Below are pupil sizes from two samples: 8 men and 8 women (measured in millimeters). Test the hypothesis that there is a difference in pupil sizes between males and females, using an alpha level of .01. 𝑠 𝑥1−𝑥2 = 𝑆𝑆 1 + 𝑆𝑆 2 𝑛 1 + 𝑛 2 −2 1 𝑛 1 + 1 𝑛 2 What is the appropriate statistical test? Report the null hypothesis. Report the alternative hypothesis. Find the critical value: Calculate the obtained statistic: Make a decision. What does your decision mean? Independent-samples t-test males females 7.7 8.9 7.5 8.7 6.9 9.0 7.8 8.8 7.9 4.5 There is not a diff in pupil size between males and females. There is a diff in pupil size between male and females. +/- 2.977 𝑡 𝑜𝑏𝑡 = 𝑥 1 − 𝑥 2 𝑠 𝑥1−𝑥2 = 7.06−8.76 SS 8.36 .94 N 8

Below are pupil sizes from two samples: 8 men and 8 women (measured in millimeters). Test the hypothesis that there is a difference in pupil sizes between males and females, using an alpha level of .01. 𝑠 𝑥1−𝑥2 = 8.36+.94 8+8−2 1 8 + 1 8 What is the appropriate statistical test? Report the null hypothesis. Report the alternative hypothesis. Find the critical value: Calculate the obtained statistic: Make a decision. What does your decision mean? Independent-samples t-test males females 7.7 8.9 7.5 8.7 6.9 9.0 7.8 8.8 7.9 4.5 There is not a diff in pupil size between males and females. There is a diff in pupil size between male and females. +/- 2.977 𝑡 𝑜𝑏𝑡 = 𝑥 1 − 𝑥 2 𝑠 𝑥1−𝑥2 = 7.06−8.76 SS 8.36 .94 N 8

Below are pupil sizes from two samples: 8 men and 8 women (measured in millimeters). Test the hypothesis that there is a difference in pupil sizes between males and females, using an alpha level of .01. 𝑠 𝑥1−𝑥2 = 9.30 14 2 8 What is the appropriate statistical test? Report the null hypothesis. Report the alternative hypothesis. Find the critical value: Calculate the obtained statistic: Make a decision. What does your decision mean? Independent-samples t-test males females 7.7 8.9 7.5 8.7 6.9 9.0 7.8 8.8 7.9 4.5 There is not a diff in pupil size between males and females. There is a diff in pupil size between male and females. +/- 2.977 𝑡 𝑜𝑏𝑡 = 𝑥 1 − 𝑥 2 𝑠 𝑥1−𝑥2 = 7.06−8.76 SS 8.36 .94 N 8

Below are pupil sizes from two samples: 8 men and 8 women (measured in millimeters). Test the hypothesis that there is a difference in pupil sizes between males and females, using an alpha level of .01. 𝑠 𝑥1−𝑥2 = .17 What is the appropriate statistical test? Report the null hypothesis. Report the alternative hypothesis. Find the critical value: Calculate the obtained statistic: Make a decision. What does your decision mean? Independent-samples t-test males females 7.7 8.9 7.5 8.7 6.9 9.0 7.8 8.8 7.9 4.5 There is not a diff in pupil size between males and females. There is a diff in pupil size between male and females. +/- 2.977 𝑡 𝑜𝑏𝑡 = 𝑥 1 − 𝑥 2 𝑠 𝑥1−𝑥2 = 7.06−8.76 SS 8.36 .94 N 8

Below are pupil sizes from two samples: 8 men and 8 women (measured in millimeters). Test the hypothesis that there is a difference in pupil sizes between males and females, using an alpha level of .01. 𝑠 𝑥1−𝑥2 = .41 What is the appropriate statistical test? Report the null hypothesis. Report the alternative hypothesis. Find the critical value: Calculate the obtained statistic: Make a decision. What does your decision mean? Independent-samples t-test males females 7.7 8.9 7.5 8.7 6.9 9.0 7.8 8.8 7.9 4.5 There is not a diff in pupil size between males and females. There is a diff in pupil size between male and females. +/- 2.977 𝑡 𝑜𝑏𝑡 = 𝑥 1 − 𝑥 2 𝑠 𝑥1−𝑥2 = 7.06−8.76 SS 8.36 .94 N 8

Below are pupil sizes from two samples: 8 men and 8 women (measured in millimeters). Test the hypothesis that there is a difference in pupil sizes between males and females, using an alpha level of .01. What is the appropriate statistical test? Report the null hypothesis. Report the alternative hypothesis. Find the critical value: Calculate the obtained statistic: Make a decision. What does your decision mean? Independent-samples t-test males females 7.7 8.9 7.5 8.7 6.9 9.0 7.8 8.8 7.9 4.5 There is not a diff in pupil size between males and females. There is a diff in pupil size between male and females. +/- 2.977 𝑡 𝑜𝑏𝑡 = 𝑥 1 − 𝑥 2 𝑠 𝑥1−𝑥2 = 7.06−8.76 .41 = -4.15 SS 8.36 .94 N 8 Reject the null hypothesis. There is a diff in pupil size between male and females.

In a specific population, there are just as many females as males In a specific population, there are just as many females as males. Forbes magazine publishes an article that 11 out of 15 of the wealthiest individuals in this population are male. I would like to test the hypothesis that the wealthiest individuals in this population are male (using alpha=.01). What is the appropriate statistical test? Report the null hypothesis. Report the alternative hypothesis. Find the critical value: Calculate the obtained statistic: Make a decision. What does your decision mean? Sign test It is not the case that the wealthiest individuals are male. The wealthiest individuals are male.

.0139 .0032 .0005 .0000

.0032 .0005 .0000

In a specific population, there are just as many females as males In a specific population, there are just as many females as males. Forbes magazine publishes an article that 11 out of 15 of the wealthiest individuals in this population are male. I would like to test the hypothesis that the wealthiest individuals in this population are male (using alpha=.01). What is the appropriate statistical test? Report the null hypothesis. Report the alternative hypothesis. Find the critical value: Calculate the obtained statistic: Make a decision. What does your decision mean? Sign test It is not the case that the wealthiest individuals are male. The wealthiest individuals are male. 13 11

.0032 .0005 .0000

In a specific population, there are just as many females as males In a specific population, there are just as many females as males. Forbes magazine publishes an article that 11 out of 15 of the wealthiest individuals in this population are male. I would like to test the hypothesis that the wealthiest individuals in this population are male (using alpha=.01). What is the appropriate statistical test? Report the null hypothesis. Report the alternative hypothesis. Find the critical value: Calculate the obtained statistic: Make a decision. What does your decision mean? Sign test It is not the case that the wealthiest individuals are male. The wealthiest individuals are male. 13 11 Retain the null hypothesis. It is not the case that the wealthiest individuals are male.

Paired-samples t-test A feline researcher would like to evaluate the effect of catnip on motor activity in kittens. He puts 5 kittens in a playpen and counts how many times each kitten swats at a hanging toy placed in the middle of the pen. He then exposes the kittens to catnip and again lets them play in the pen and counts the number of swats. Test the hypothesis that catnip has an effect on motor activity in kittens using an alpha of .01. Assume a normal distribution. No catnip catnip 5 8 7 9 6 1 What is the appropriate statistical test? Report the null hypothesis. Report the alternative hypothesis. Find the critical value: Calculate the obtained statistic: Make a decision. What does your decision mean? Paired-samples t-test Catnip does not have an effect on motor activity. Catnip has an effect on motor activity.

two-tailed a=.01 4 df

𝑡 𝑜𝑏𝑡 = 𝐷 𝑠 𝐷 = −1.2 .73 𝑠 𝐷 = 𝑆𝑆 𝐷 𝑁(𝑁−1) 𝑠 𝐷 = 10.8 20 = .73 A feline researcher would like to evaluate the effect of catnip on motor activity in kittens. He puts 5 kittens in a playpen and counts how many times each kitten swats at a hanging toy placed in the middle of the pen. He then exposes the kittens to catnip and again lets them play in the pen and counts the number of swats. Test the hypothesis that catnip has an effect on motor activity in kittens using an alpha of .01. Assume a normal distribution. 𝑠 𝐷 = 𝑆𝑆 𝐷 𝑁(𝑁−1) 𝑆𝑆 𝐷 = 𝐷 2 − 𝐷 2 𝑁 No catnip catnip 5 8 7 9 6 1 D -3 -2 1 What is the appropriate statistical test? Report the null hypothesis. Report the alternative hypothesis. Find the critical value: Calculate the obtained statistic: Make a decision. What does your decision mean? Paired-samples t-test Catnip does not have an effect on motor activity. Catnip has an effect on motor activity. 𝑆𝑆 𝐷 =18− −6 2 5 +/- 4.604 𝑡 𝑜𝑏𝑡 = 𝐷 𝑠 𝐷 = −1.2 .73 𝑆𝑆 𝐷 =18−7.2 𝑆𝑆 𝐷 =10.8 𝑠 𝐷 = 10.8 20 = .73

A feline researcher would like to evaluate the effect of catnip on motor activity in kittens. He puts 5 kittens in a playpen and counts how many times each kitten swats at a hanging toy placed in the middle of the pen. He then exposes the kittens to catnip and again lets them play in the pen and counts the number of swats. Test the hypothesis that catnip has an effect on motor activity in kittens using an alpha of .01. Assume a normal distribution. No catnip catnip 5 8 7 9 6 1 D -3 -2 1 What is the appropriate statistical test? Report the null hypothesis. Report the alternative hypothesis. Find the critical value: Calculate the obtained statistic: Make a decision. What does your decision mean? Paired-samples t-test Catnip does not have an effect on motor activity. Catnip has an effect on motor activity. +/- 4.604 𝑡 𝑜𝑏𝑡 = 𝐷 𝑠 𝐷 = −1.2 .73 =−1.64 Retain the null hypothesis. Catnip does not affect motor activity.