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.

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	Adults aged 20 to 29			Adults aged 30 to 39
	x1			x2
	n1			n2
	p1			p2

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.

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.

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
x-bar1			x-bar2
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

T-statistics

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.