Statistics Question

Module 05 Content

1.

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.

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.

1. Population Proportions
Nightingale Shoes is trying to determine the demographic who is purchasing their shoes. After
find that 205 out of 369 adults between the age of 20 to 29 were purchasing their shoes. They also discover
to 39 were purchasing their shoes. Test the claim that younger adults (aged 20 to 29) purchase more Nightin
to 39). Assume a 0.01 significance.
Adults aged 20 to 29
x1
Adults aged 30 to 39
x2
n1
n2
ෞ𝟏
𝒑
ෞ𝟐
𝒑
1a. Write the hypotheses in symbolic form, determine if the test is right-tailed, left-tailed, or two tailed and explain
1b. Calculate the pooled sample proportion and the test statistic.
Explain your calculations and include your results.
Pooled Sample Proportion
q-bar
Test Statistic
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.
Critical Value
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.
p-value
1e. Restate your conclusion in nontechnical terms.
their shoes. After surveying customers who enter their store, they
their shoes. They also discovered that 105 out of 213 adults aged 30
20 to 29) purchase more Nightingale shoes than older adults (aged 30
tailed, or two tailed and explain why.
2. Population Means – Independent Samples
Nightingale shoes is interested to know who is spending more on their brand: women or men. They surveye
entered their store. They found that 89 men on average spent $65 with a standard deviation of $6. On the o
$72 with a standard deviation of $23. Test the claim that women spend more on Nightingale shoes then me
level and the population standard deviations are unknown.
Men Spending
n1
s1
Women Spending
n2
s2
2a. Write the hypotheses in symbolic form, determine if the test is right-tailed, left-tailed, or two tailed and explain
2b. Calculate the critical value, the test statistic, and p-value. Show calculations below.
Explain your calculations and include your results.
Critical Value
Test Statistic
p-value
2c. Make a decision about the null hypothesis using both the Critical Value and P-Value Methods.
Explain how you arrived at your results.
2d. Restate your conclusion in nontechnical terms.
women or men. They surveyed the first 200 people who
dard deviation of $6. On the other hand, 111 women spent
on Nightingale shoes then men. Assume a 0.05 significance
tailed, or two tailed and explain why.
Methods.
3. Population Means – Dependent Samples
Nightingale shoes is looking at the productivity of a sample of its stores. They look at the average number o
and compare the results with the average number of shoe sales per month in 2020. Based on the data in the
that the average number of monthly shoe sales is more in 2019 than in 2020 using a 0.1 significance level. A
standard deviations are unknown.
Month
January
Febrary
March
April
May
June
July
August
September
October
November
December
2019
2187
2722
3383
3043
3018
2796
3093
3988
2594
2721
3038
4044
2020
2148
2701
1686
462
1624
2692
2722
2822
2643
2677
2617
3824
n
df
𝑑ҧ
sd
3a. Write the hypotheses in symbolic form, determine if the test is right-tailed, left-tailed, or two tailed and explai
3b. Calculate the critical value, the test statistic, and p-value. Show calculations below.
Explain your calculations and include your results.
Critical Value
Test Statistic
p-value
3c. Make a decision about the null hypothesis using both the Critical Value and P-Value Methods.
Explain how you arrived at your results.
3d. Restate your conclusion in nontechnical terms.
ook at the average number of shoe sales per month in 2019
2020. Based on the data in the table below, test the claim
sing a 0.1 significance level. Assume that the population
tailed, or two tailed and explain why.
Methods.