1. MATH 2311
Week 14 (Test 3 Review)

3. A SRS of 81 observations produced a mean of 250 with a standard deviation of 22. Determine the 95% confidence interval for the population mean.

4. A random sample of 64 observations produced a sample proportion of 0
A random sample of 64 observations produced a sample proportion of Determine the 95% confidence interval for the population proportion.

5. After performing a p-test, the P-Value is found to be smaller than the significance level. How should you proceed?

6. Which of the following will increase the width of the sample mean?
Decrease the sample size
Increase the confidence level
Increase the sample size
Decrease the confidence level
Increase the value of the mean
Decrease the value of the mean

7. The weights of pennies produced by the US Mint is determined to have a standard deviation of 0.2 grams. You wish to create a mean confidence interval of level 90%. How large of a sample of pennies should you select to have a margin of error of .02?

8. A one-sample z-statistic for a test of Ho: μ=53, and Ha: μ>53 based of 75 observations is z = Determine the p-value.

9. An assortment of candies claims that their sample bag contains the following: 15% Snickers, 35% Milky Way, 25% Three Musketeers, 15% Almond Joy and 10% Mounds. From a bag of 200 candies, you find there are 30 Snickers, 35 Milky Way, 40 Three Musketeers, 45 Almond Joy and 50 Mounds. What type of test should you run, and what is the test statistic?

10. Various studies state that, worldwide, 1% of persons suffer from Autism. You believe that this number should be higher. You take an SRS of 500 people and find that 8 people have Autism. Test your claim with 5% significance.
Determine your Null and Alternate Hypothesis.

11. Various studies state that, worldwide, 1% of persons suffer from Autism. You believe that this number should be higher. You take an SRS of 500 people and find that 8 people have Autism. Test your claim with 5% significance.
Determine your rejection region.

12. Various studies state that, worldwide, 1% of persons suffer from Autism. You believe that this number should be higher. You take an SRS of 500 people and find that 8 people have Autism. Test your claim with 5% significance.
Calculate your test statistic.

13. Various studies state that, worldwide, 1% of persons suffer from Autism. You believe that this number should be higher. You take an SRS of 500 people and find that 8 people have Autism. Test your claim with 5% significance.
Determine your p-value.

14. Various studies state that, worldwide, 1% of persons suffer from Autism. You believe that this number should be higher. You take an SRS of 500 people and find that 8 people have Autism. Test your claim with 5% significance.
Draw a conclusion.

15. It is determined that the mean number of car accidents teenage drivers experience is 4. You collect data from 20 twenty-year olds and find their mean number of accidents was 6.3 with a standard deviation of Test, with a significance of 5%, if there is doubt in the accepted mean.
Determine your Null and Alternate Hypothesis.

16. It is determined that the mean number of car accidents teenage drivers experience is 4. You collect data from 20 twenty-year olds and find their mean number of accidents was 6.3 with a standard deviation of Test, with a significance of 5%, if there is doubt in the accepted mean.
Determine your rejection region.

17. It is determined that the mean number of car accidents teenage drivers experience is 4. You collect data from 20 twenty-year olds and find their mean number of accidents was 6.3 with a standard deviation of Test, with a significance of 5%, if there is doubt in the accepted mean.
Calculate your test statistic.

18. It is determined that the mean number of car accidents teenage drivers experience is 4. You collect data from 20 twenty-year olds and find their mean number of accidents was 6.3 with a standard deviation of Test, with a significance of 5%, if there is doubt in the accepted mean.
Determine your p-value.

19. It is determined that the mean number of car accidents teenage drivers experience is 4. You collect data from 20 twenty-year olds and find their mean number of accidents was 6.3 with a standard deviation of Test, with a significance of 5%, if there is doubt in the accepted mean.
Draw a conclusion.

20. A simple random sample of 10 students was selected to determine their commuting distance. The results are as follows: Determine the 95% confidence interval for the true population mean.

21. A simple random sample of 1000 students was selected to determine if they worked full-time while attending college full-time. Of the 1000 students 722 reported working full time. Determine the 90% confidence interval for the population proportion.

22. If the p-value in is larger than the confidence level, the researcher should (a) Accept the Ho, (b) Reject the Ho, (c) Fail to Reject the Ho, (d) Accept the Ha

23. You have created a confidence interval
You have created a confidence interval. When repeating the study, the width of the confidence interval has decreased. Which of the following may be also true:
The confidence level has decreased.
The sample size has decreased.
The sample parameter has increased
The margin of error has decreased.
The standard deviation or standard error has increased.

24. A population has a standard deviation of 0. 03
A population has a standard deviation of You are selecting a sample to find the population mean with a confidence level of 95%. How large of a population should you select if you want a margin of error less than 0.004?

25. You run an experiment to test where Ho: 𝑝 = 0. 34 and Ha: 𝑝 ≠. 34
You run an experiment to test where Ho: 𝑝 = 0.34 and Ha: 𝑝 ≠ .34. The value of your test statistic is z = Determine the p-value.

26. A cereal company claims that their marshmallow cereal contains the following shapes: An actual box of cereal contained the following pieces: Determine the test type and the test statistic for this example.

27. A prep school claims that 85% of their graduates are accepted to Ivy League schools. You believe that the proportion is less than that. To investigate, you find an SRS of 350 of their graduates and discover that 265 of them were accepted into Ivy League schools. We will test the claim at a 2% significance level.
State the null and alternate hypothesis:

28. A prep school claims that 85% of their graduates are accepted to Ivy League schools. You believe that the proportion is less than that. To investigate, you find an SRS of 350 of their graduates and discover that 265 of them were accepted into Ivy League schools. We will test the claim at a 2% significance level.
Sketch and state the rejection region.

29. A prep school claims that 85% of their graduates are accepted to Ivy League schools. You believe that the proportion is less than that. To investigate, you find an SRS of 350 of their graduates and discover that 265 of them were accepted into Ivy League schools. We will test the claim at a 2% significance level.
Calculate the test statistic.

30. A prep school claims that 85% of their graduates are accepted to Ivy League schools. You believe that the proportion is less than that. To investigate, you find an SRS of 350 of their graduates and discover that 265 of them were accepted into Ivy League schools. We will test the claim at a 2% significance level.
Determine the p-value for your test.

31. A prep school claims that 85% of their graduates are accepted to Ivy League schools. You believe that the proportion is less than that. To investigate, you find an SRS of 350 of their graduates and discover that 265 of them were accepted into Ivy League schools. We will test the claim at a 2% significance level.
State your conclusion.

32. A study shows that a family of four, on average, spends $255 per week on groceries. You believe that this amount is incorrect. To test your hypothesis, you select 35 local families of four and calculate their average grocery budget to be $295 with a standard deviation of $12.3 Test this claim using a significance level of 5%.
State your null and alternate hypothesis

33. A study shows that a family of four, on average, spends $255 per week on groceries. You believe that this amount is incorrect. To test your hypothesis, you select 35 local families of four and calculate their average grocery budget to be $295 with a standard deviation of $12.3 Test this claim using a significance level of 5%.
Sketch and state the rejection region.

34. A study shows that a family of four, on average, spends $255 per week on groceries. You believe that this amount is incorrect. To test your hypothesis, you select 35 local families of four and calculate their average grocery budget to be $295 with a standard deviation of $12.3 Test this claim using a significance level of 5%.
Calculate your test statistic.

35. A study shows that a family of four, on average, spends $255 per week on groceries. You believe that this amount is incorrect. To test your hypothesis, you select 35 local families of four and calculate their average grocery budget to be $295 with a standard deviation of $12.3 Test this claim using a significance level of 5%.
Calculate your p-value.

36. A study shows that a family of four, on average, spends $255 per week on groceries. You believe that this amount is incorrect. To test your hypothesis, you select 35 local families of four and calculate their average grocery budget to be $295 with a standard deviation of $12.3 Test this claim using a significance level of 5%.
Draw your conclusion.

37. Popper 12:
Answer Choice A for Questions 1 – 10.