PROBLEM 1: Creating Confidence Interval Estimate for the Population Mean

Trivago, the global travel search platform, is interested in the average price of a hotel room during the summer in a resort community. A random sample of 25 hotels from the community is taken and the average price for a regular room with a king size bed was found to be $215 with a population standard deviation of $30.

1. Construct a 95% confidence interval estimate for the mean price for a hotel room in this resort community. Show your work in the space below:

2. Suppose the confidence level of your study changes to 99%. Assuming all other elements of your study held constant, the confidence interval estimate will become.... (Circle one)

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3. Suppose the sample size of your study changes to only 15 hotels. Assuming all other elements of your study held constant, the confidence interval estimate will become... (Circle one)

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PROBLEM 2: Creating Confidence Interval Estimate for the Population Proportion

A company is studying consumer preferences for 3 product designs. A random sample of 200 consumers is taken. Of this sample, 90 consumers prefer Design A, 60 consumers prefer Design B, and the remaining 50 consumers prefer Design C.

1. Calculate the proportion of the sample of 200 consumers who prefer Design B. Show your work in the space below:

2. Using your calculation for the sample proportion who prefer Design B, construct a 95% confidence interval estimate for the proportion of all consumers that prefer Design B. Show your work in the space below.

3. Suppose that you repeated this study but increased the sample size to 500 consumers. Assuming all other elements of your study held constant, the confidence interval estimate would become... (Circle one)

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PROBLEM 3: Determining Sample Size for a Study of the Proportion

A company would like to determine the repurchase rate for a new product that was just launched. A sample of 95 consumers who purchased the product is taken. The consumers were asked, "Do you plan to purchase this product again?" Out of the sample of 95 consumers, 38 consumers answered "Yes". The results in the form of Minitab output is shown below. The 95% Confidence Interval estimate is shown in the red circle.

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Test and CI for One Proportion: Purchase Intent

Event = YES

Variable X N Sample p 95% CI

REPURCHASE 38 95 0.400000 (0.30, 0.50)

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QUESTION: As you can see the width of the 95% confidence interval is quite large (10%). You would like to reduce the margin of error of this study to 4%. You decide to take a larger sample size to reduce your margin of error. While remaining at a 95% confidence level, calculate the required sample size you must take to reduce your margin of error to within 4% of the true proportion. (Hint: Refer to Slide 33 of WEEK 3 Slides to find the formula for Sample Size Determination for a Proportion). Show your calculations and final answer below: