Question

A researcher is interested in finding a 98% confidence interval for the mean number of times per day that college students text. The study included 142 students who averaged 30.3 texts per day. The standard deviation was 18.9 texts. Round answers to 3 decimal places where possible.

a. To compute the confidence interval use a distribution.

b. With 98% confidence the population mean number of texts per day is between answer _______ and answer _______ texts.

c. If many groups of 142 randomly selected members are studied, then a different confidence interval would be produced from each group. About answer __________ percent of these confidence intervals will contain the true population number of texts per day and about answer _______ percent will not contain the true population mean number of texts per day.

Answer 1

a)Given the sample mean is   , sample standard deviation and sample size is .

The confidence interval for true mean based on the sample mean is

Since the population standard deviation is not known, we use t-distribution.

So the 98% CI for mean is

b)We are sure with 98% confidence that the true number of texts lies in the interval .

With 98% confidence the population mean number of texts per day is between answer ___26.57____ and answer __34.03_____ texts.

c) About answer ____98%______ percent of these confidence intervals will contain the true population number of texts per day and about answer ___2%____ percent will not contain the true population mean number of texts per day.