question 1:

A survey of 800 employees indicated that 45% of males and 33% of females prefer to work from home. Assume that the survey consisted of 400 males and 400 females. At the .10 level of significance, is there evidence of a difference in the proportion of males and females who prefer to work from home?

1. Specify the null hypothesis and the alternative hypothesis. State whether you are using a one- or two-tailed test and explain your reasoning.
2. Determine the appropriate hypothesis test to this problem. Justify your answer
3. Conduct calculations by hand to compute the critical value and p-value of the test. Determine your decision using two methods, the rejection region and the p-value approach.
4. Use R to conduct the hypothesis test. Copy and paste the command and output generated by R.
5. Communicate the results of the test in "plain English" including the meaning of the p-value.

question 2:

https://docs.google.com/spreadsheets/d/1S-Fe_NQS-twH0CRP-WXPchfOLUcRdkTz/edit?usp=sharing&ouid=113068968791942309329&rtpof=true&sd=true

A bank has the business objective of improving the process for servicing customers during the noon-to-1PM lunch period. To do so, the waiting time (defined as the number of minutes that elapses from when the customer enters the line until he or she reaches the teller window) needs to be shortened to increase customer satisfaction. A random sample of customers at two different branches of the bank is selected and the waiting times are collected and stored in the file BankTimes.xlsx.

Is there evidence that the mean waiting time in Branch 1 is less than in Branch 2?

1. Specify the null hypothesis and the alternative hypothesis. State whether you are using a one- or two-tailed test and explain your reasoning.
2. Determine the appropriate hypothesis test to this problem. Justify your answer.
3. Conduct calculations by hand to compute the critical value and p-value of the test. Determine your decision using two methods, the rejection region and the p-value approach.
4. Use R to conduct the hypothesis test. Copy and paste the command and output generated by R.
5. Communicate the results of the test in "plain English" including the meaning of the p-value.

question 3:

https://docs.google.com/spreadsheets/d/1VJBETC3lTr6Chg3waLpRXmrtnKMxNRjM/edit?usp=sharing&ouid=113068968791942309329&rtpof=true&sd=true

A real estate agent has collected a random sample of 75 houses that were recently sold in a suburban community. She is particularly interested in comparing the appraised value and recent selling price of the houses in this particular market. The data are provided in the fileReal_Estate.xlsx.

1. Using R calculate summary statistics and a correlation table for the data. Copy and paste the results.
2. What test is more appropriate (a two-sample test or a paired test) to assess whether there is evidence of a mean difference in the appraised values and selling prices? Explain your reasoning.
3. Using this sample data, test whether there is a statistically significant mean difference between the appraised values and selling prices of the houses sold in this suburban community.
4. Set up the appropriate null and alternative hypothesis for this situation. Specify whether this is a one-tailed test or a two-tailed test and explain your reasoning.
5. Use R to conduct the test and compute the p-value for your test statistic. For which level of significance is it appropriate to conclude that no difference exists between these two values? Copy and paste the output generated by R.
6. Communicate the results of the test in plain English within the context of the problem.