Please can you show the answer of all questions with steps shown, explanations, and correct formatting.

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 significancant

Adults aged 20-29	Adults aged 30-39
x1	x1
n1	n2
(p_1 )	(p_2 )

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.

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.

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.

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.

Men Spending	Women spending
n1	n2
x1	x2
s1	s2

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.

	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.

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

Month	2019	2020
January	2187	2148
FEB	2722	2701
March	3388	1686
April	3043	462
May	3018	1624
June	2796	2692
July	3093	2722
August	3988	2822
September	2594	2643
October	2721	2677
November	3038	2617
December	4044	3824

n

df

s_d

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.

	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.