The branch manager of a nationwide bookstore chain wants to study characteristic

Question

The branch manager of a nationwide bookstore chain wants to study characteristics of her store's customers. She decides to focus on two variables: the amount of money spent by customers and whether the customers would consider purchasing educational videotapes relating to graduate preparation exams such as GMAT, GRE, or LSAT. The results from a sample of 70 customers are as follows: Amount spent: X = $28.52, S = $11.39. Construct a 95% confidence interval estimate of the population mean amount spent in the bookstore. An automobile dealer wants to estimate the proportion of customers who still own the cars they purchased five years earlier. A random sample of 200 customers selected from the automobile dealer's records indicates that 82 still own cars that were purchased five years earlier.

Explanation / Answer

Let X be the random variable that amount spent in the bookstore.

Here we have to find 95% confidence interval for population mean amount spent in the bookstore.

Here sample standard deviation is known so we use one sample t-interval.

95% confidence interval for population mean is,

Xbar -E < mu < Xbar + E

where Xbar = 28.52

E is margin of error.

E = (tc * s) /sqrt(n)

tc is critical value for t-distribution.

s = 11.39

n = 71

We can find confidence interval by using TI-83 calculator.

steps :

STAT --> TESTS --> 8:TInterval --> ENTER --> Highlight on Stats --> ENTER --> Input all the values --> Calculate --> ENTER

95% confidence interval for population mean is (25.824, 31.216).

We are 95% confident that the population mean is lies between 25.824 and 31.216.

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