   Chapter 6, Problem 6.7P

Chapter
Section
Textbook Problem

S O C A random sample of 429 college students was interviewed about a number of matters. Use the results to construct confidence interval estimates of the population mean at the 99% level.a. They reported that they had spent an average of $478.23 on textbooks during the previous semester, with a sample standard deviation of$ 15.78 .b. They also reported that they had visited the health clinic an average of 1.5 times a semester, with a sample standard deviation of 0.3.c. On the average, the sample had missed 2.8 days of classes per semester because of illness, with a sample standard deviation of 1.0.d. On the average, the sample had missed 3.5 days of classes per semester for reasons other than illness, with a sample standard deviation of 1.5.

To determine

a)

To find:

The 99% confidence interval for the population mean.

Explanation

Given:

The given information is,

A random sample of 429 college students was interviewed about a number of matters.

They reported that they had spent an average of $478.23 on textbooks during the previous semester, with a sample standard deviation of$15.78.

Description:

The confidence interval is an interval estimate from the statistics of the observed data that might contain the true value of the unknown population parameter.

Formula used:

For large samples and given sample standard deviation, the confidence interval (c.i.) for population mean is given by,

c.i.=X¯±Z(sN1)

Where, X¯ is the sample mean,

s is the sample standard deviation,

Z is the Z score determined by the alpha level and,

N is the sample size.

Calculation:

From the given information, the sample size is 429, sample mean is $478.23 and the sample standard deviation is$15.78.

For 99%, the Z value is given as,

Z(99%)=2.58

For large samples and given sample standard deviation, the confidence interval (c

To determine

b)

To find:

The 99% confidence interval for the population mean.

To determine

c)

To find:

The 99% confidence interval for the population mean.

To determine

d)

To find:

The 99% confidence interval for the population mean.

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