introduction to statistics

7. A researcher has a sample of 24 people.
a) If conducting a 99% confidence interval, what is the critical value?
b) If conducting a 95% confidence interval, what is the critical value?
c) If conducting a 90% confidence interval, what is the critical value?
d) If the researcher obtains another sample of 62 people, how does that affect the critical value?
8. When conducting a hypothesis test (of a mean or proportion) with a large sample (n = 350), what is the critical value:
a) For a one-tailed test at alpha 0.01?
b) For a two- tailed test at alpha 0.01?
c) For a one tailed test at alpha 0.05?
d) For a two-tailed test at alpha 0.001?
e) For a one-tailed test at alpha 0.10?
9. A researcher is interested in understanding peoples’ commitment to the environment so asks the following question: “Would you be willing to pay higher taxes in order to protect the environment?” Of the 800 people randomly surveyed, 452 people said No and 348 answered Yes. Based on previous GSS data, the population proportion that is willing to pay higher taxes is .40. Conduct the appropriate test to determine if the sample proportion is greater than that of the population.
a) List all the steps needed to conduct the appropriate test using alpha level of 0.05 to make your decision.
10. Data suggests that the average income for fully employed Canadians was $64,630 in 2020. A random sample of 125 BC residents finds that their average income was $68,000 with a standard deviation of $9,800. Conduct a test to determine whether it is plausible that BC residents have a higher average income than the Canadian population.
a) Show all the steps needed to conduct the appropriate test, using a significance level of 0.05 to make your decision.
11. Below is information on average weekly exercise for Sociology and Psychology students.
Sociology weekly exercise = 6.75, standard deviation = 1.4, n = 23
Psychology weekly exercise = 5.72, standard deviation = 1.6, n = 24
Conduct an appropriate test to determine if mean weekly exercise differs between Sociology and Psychology students.
a) Write out the null and research hypothesis of this test.
b) Calculate the appropriate test statistic
c) What is your decision and conclusion about the difference in average exercise at alpha/significance level of 0.05?
d) Does your decision and conclusion change if alpha is set at 0.01? If yes, why and how?