Chapter 7 Statistics Power Point Review Hypothesis Testing

The mean IQ of statistics teachers is 120. Mr. Cook believes the IQ is greater. Write the null and alternative hypotheses. Define the parameter.

Answer: left-tailed

In the left tail

The mean IQ of statistics teachers is 120. Mr. Cook believes the IQ is greater. Identify the type I and type II errors for the hypothesis test of this claim. Type I errors occur when we reject the null hypothesis when it is actually true (RT1). We said there was insufficient evidence to support the mean IQ of statistics teachers is 120 when it really is. Type II errors occur when we fail to reject the null hypothesis when it is actually false (FF2). We said there was sufficient evidence to support that the mean IQ of statistics teachers is 120 when it actually is not.

Since this is a right-tailed test, the P-value will be located in the right tail. We can go to the z-table and find the area to the left of The area to the left is

Answer:C

We have a sample size of 25 with a population standard deviation of 5.5. Which type of test will we use? The t-test or the z-test? Even though the sample size is less than 30, we know the population standard deviation, so we will use the… Z-test

We have a sample size of 50 with a sample standard deviation of 30. Which type of test will we use? The t-test or the z-test?

We have a sample size of 20 with a sample standard deviation of 5.5. Which type of test will we use? The t-test or the z-test? Our sample size is less than 30 and the population standard deviation is unknown. We will use the… T-test

Since the P-value is higher than the level of significance, we… Fail to reject the null hypothesis.

Larson/Farber 4th ed. 13 When the p-value is lower than the alpha level, we reject the null hypothesis and use the alternative hypothesis “When it’s low, let it go…reject the null.” When the p-value is higher than the alpha level, we fail to reject the null hypothesis. “When it’s high, let it fly…we fail to reject the null hypothesis.”

“Since the p-value ) , we reject (fail to reject) the H 0. There is (is not) sufficient evidence to suggest that H a.” Be sure to write H a in context (words)!

Examples of Decision & Interpreting When Testing A Claim We reject the null hypothesis. We have sufficient evidence to reject the claim that the true proportion of home buyers who found a real estate agent through a friend is 44%. We reject the null hypothesis. We have sufficient evidence to support that the true proportion of home buyers who found a real estate agent through a friend differs from 44%. We reject the null hypothesis. We have insufficient evidence to support the claim that the true proportion of home buyers who found a real estate agent through a friend is 44%.

Examples of Decision & Interpreting When Testing A Claim We fail to reject the null hypothesis. We have sufficient evidence support the claim that the true proportion of home buyers who found a real estate agent through a friend is 35%. We fail to reject the null hypothesis. We have sufficient evidence to support that the true proportion of home buyers who found a real estate agent through a friend does not differ from 35%. We fail to reject the null hypothesis. We have insufficient evidence to support the claim that the true proportion of home buyers who found a real estate agent through a friend differs from 35%.

The area in the left tail is 0.05, so go to the z-table and locate the area for C.V.

The area in both tails total We must split this area in half, which will equal.005. Go to the z-table and locate the area to the left of

C.V.

This is a left-tailed test. Will we use the z-test or t-test for the population mean?

This is a left-tailed test, so the z-score will be negative. Find the P-value in the z-table. The P-value is.2148 Compare the P-value,.2148, to the alpha level, The P-value is higher than the alpha level, so what decision will we make?

What is our tail type?A right-tailed test What is our sample size?10 So the rejection region will be to the … right What type of test will we use? The z-test or t-testThe t-test What do we need to know for the t-test?Degrees of freedom Go to the t-table and match up your alpha level with the degrees of freedom. Answer: 1.833

What is our tail type?A left-tailed test So the rejection region will be to the … left What is our sample size?12 What type of test will we use? The z-test or t-test Do we know the population standard deviation?No The t-test

We now need to find the standardized test statistic, t.

This is a left-tailed test. Will we use the z-test or t-test for the population mean?

C.V. The area in the tail is We need to find the critical value that separates the rejection region (in red) from the non rejection region.

C.V. We need to find the standardized test statistic, t. Where does the t-statistic fall? The rejection or non rejection region? The non rejection region We will fail to reject the null hypothesis. We have insufficient evidence to support the mean lifetime of its fluorescent bulbs is less than 1100 hours.

Test the conditions We cannot use the normal sampling distribution since both conditions are not met.

This is a two-tailed test. How many critical values do we have?2 What is the total area in the two tails? 0.05 What is the area in each of the two tails? 0.025

Find the z-score that matches up with Use the z-table or InvNorm.

This is a two-tailed test. We first need to check the conditions as to whether we can use the normal sampling distribution.

The conditions are met, so we can use the normal sampling distribution.

We can now calculate our standardized test statistic.

The engineering school at a major university claims that 20% of its graduates are women. We differ with this claim. In a sample of 210 students, 58 were women. We reject the null hypothesis. We have sufficient evidence to support the graduation rate of women in the engineering school at a major university is different than 20%.