Scenario
Nightingale Shoes has hired you to run consulting work for their company. They need to understand the demographic and gender that is purchasing their shoes to determine how they should advertise. They also need you to compare their shoe sales during two different years.
The spreadsheet below contains three hypothesis tests to run.
Deliverable 5 – Hypothesis Tests for Two Samples
Instructions
Work through each hypothesis test in the spreadsheet above and answer all questions provided. Note that each question is presented on a separate tab in the spreadsheet.
You must submit the spreadsheet with the completed calculations, answers, and analysis. Ensure that you are completely answering all questions with steps shown, explanations, and correct formatting.
Question 1
| Adults aged 20 to 29 | Adults aged 30 to 39 | ||||
| x1 | x2 | ||||
| n1 | n2 | ||||
| Pooled Sample Proportion | |||||
| q-bar | |||||
| Test Statistic | |||||
| Critical Value | |||||
| p-value |
1. Population Proportions Nightingale Shoes is trying to determine the demographic who is purchasing their shoes. After surveying customers who enter their store, they find that 205 out of 369 adults between the age of 20 to 29 were purchasing their shoes. They also discovered that 105 out of 213 adults aged 30 to 39 were purchasing their shoes. Test the claim that younger adults (aged 20 to 29) purchase more Nightingale shoes than older adults (aged 30 to 39). Assume a 0.01 significance.
1a. Write the hypotheses in symbolic form, determine if the test is right-tailed, left-tailed, or two tailed and explain why.
1b. Calculate the pooled sample proportion and the test statistic. Explain your calculations and include your results.
1c. Calculate the critical value and make a decision about the null hypothesis. Explain your calculations, include your results, and explain how you arrived at your decision.
1c. Calculate the critical value and make a decision about the null hypothesis. Explain your calculations, include your results, and explain how you arrived at your decision.
1d. Calculate the p-value and make a decision about the null hypothesis. Explain your calculations, include your results, and explain how you arrived at your decision.
1e. Restate your conclusion in nontechnical terms.
Question 2
| Men Spending | Women Spending | ||||
| n1 | n2 | ||||
| s1 | s2 | ||||
| Critical Value | |||||
| Test Statistic | |||||
| p-value |
2a. Write the hypotheses in symbolic form, determine if the test is right-tailed, left-tailed, or two tailed and explain why.
2b. Calculate the critical value, the test statistic, and p-value. Show calculations below. Explain your calculations and include your results.
2c. Make a decision about the null hypothesis using both the Critical Value and P-Value Methods. Explain how you arrived at your results.
2. Population Means – Independent Samples Nightingale shoes is interested to know who is spending more on their brand: women or men. They surveyed the first 200 people who entered their store. They found that 89 men on average spent $65 with a standard deviation of $6. On the other hand, 111 women spent $72 with a standard deviation of $23. Test the claim that women spend more on Nightingale shoes then men. Assume a 0.05 significance level and the population standard deviations are unknown.
2d. Restate your conclusion in nontechnical terms.
Question 3
| Month | 2019 | 2020 | |||||
| January | 2187 | 2148 | |||||
| Febrary | 2722 | 2701 | n | ||||
| March | 3383 | 1686 | df | ||||
| April | 3043 | 462 | |||||
| May | 3018 | 1624 | |||||
| June | 2796 | 2692 | sd | ||||
| July | 3093 | 2722 | |||||
| August | 3988 | 2822 | |||||
| September | 2594 | 2643 | |||||
| October | 2721 | 2677 | |||||
| November | 3038 | 2617 | |||||
| December | 4044 | 3824 | |||||
| Critical Value | |||||||
| Test Statistic | |||||||
| p-value | |||||||
3a. Write the hypotheses in symbolic form, determine if the test is right-tailed, left-tailed, or two tailed and explain why.
3b. Calculate the critical value, the test statistic, and p-value. Show calculations below. Explain your calculations and include your results.
3c. Make a decision about the null hypothesis using both the Critical Value and P-Value Methods. Explain how you arrived at your results.
3. Population Means – Dependent Samples Nightingale shoes is looking at the productivity of a sample of its stores. They look at the average number of shoe sales per month in 2019 and compare the results with the average number of shoe sales per month in 2020. Based on the data in the table below, test the claim that the average number of monthly shoe sales is more in 2019 than in 2020 using a 0.1 significance level. Assume that the population standard deviations are unknown.
3d. Restate your conclusion in nontechnical terms.