1. Dr. Z, an expert in consumer behavior, wants to estimate the average amount o

Question

1. Dr. Z, an expert in consumer behavior, wants to estimate the average amount of money that people spend in thrift shops. He takes a small sample of 8 individuals and asks them to report how much money they had in their pockets the last time they went shopping at a thrift store. Here are the data: 18, 37, 26, 27, 31, 11, 16, 17. Find the upper bound of a 95% confidence interval for the true mean amount of money individuals carry with them to thrift stores, to two decimal places. Take all calculations toward the final answer to three decimal places.

2. Suppose we were to gather a random sample of 7 observations from a population and wished to calculate a 90% confidence interval for the mean, µ, in the case where the population standard deviation, , is unknown. Enter the value from the Student's t distribution that we would use, to three decimal places.

3. Colleges and universities routinely examine the scores their applicants have on the ACT and SAT entrance exams for a variety of reasons. In one recent year, nationwide, scores on the ACT had a mean of 22.3 and a standard deviation of 6.1. Suppose a random sample of 20 applicants was selected from the population of all students nationwide who took the test. What is the probability that the average ACT score of this sample, top enclose Y , would be greater than 27?

4. In the U.S., it has been claimed that adults between the ages of 18 and 30 send an average of 58.8 text messages per day, with a standard deviation of 20.2. If a random sample of 123 adults in this age group were collected, what would be the standard deviation of the sampling distribution of the sample mean, to one decimal place?

5. A major chain of electronics stores is interested in estimating the true mean dollar amount that customers who have a reward card would spend on a first visit to a new store. From a database of existing card holder information, 15 accounts were randomly sampled. The sample mean amount spent was $50.50, with a standard deviation of $20. A 95% confidence interval for the true mean amount spent on a first visit would be which of the following?

Explanation / Answer

Answer to question# 1)

The sample size n = 8

Sample mean (x bar) = (18+37+26+27+31+11+16+17) / 8 = 22.875

Sample standard deviation (s) = 8.7739

.

The formula of upper bound is:

x bar + t * s/ n

we need to find the T critical value for df = 8-1 = 7 and confidence level = 0.95 from the T table

We get T critical = 2.365

Thus we plug in these values and find the upper bound

= 22.875 + 2.365 * 8.7739 / 8

= 30.21133

Thus the upper bound is 30.21133

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