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A poll of 1,200 voters asked what the most significant issue was in the upcoming election. Sixty-five percent answered the economy. We are interested in the population proportion of voters who feel the economy is the most important.

Construct a 90% confidence interval, and state the confidence interval and the error bound.

You do a study of hypnotherapy to determine how effective it is in increasing the number of hours of sleep subjects get each night. You measure hours of sleep for $12$subjects with the following results. Construct a $95$% confidence interval for the mean number of hours slept for the population (assumed normal) from which you took the data. $8.2$; $9.1$; $7.7$; $8.6$; $6.9$; $11.2$; $10.1$; $9.9$; $8.9$; $9.2$; $7.5$; $10.5$

The Ice Chalet offers dozens of different beginning iceskating classes. All of the class names are put into a bucket. The 5 P.M., Monday night, ages 8 to 12, beginning ice-skating class was picked. In that class were 64 girls and 16 boys. Suppose that we are interested in the true proportion of girls, ages 8 to 12, in all beginning ice-skating classes at the Ice Chalet. Assume that the children in the selected class are a random sample of the population.

Calculate the following:

a. x = _______

b. n = _______

c. p′ = _______

A random sample of statistics students were asked to estimate the total number of hours they spend watching television in an average week. The responses are recorded in Table $8.4$. Use this sample data to construct a $98$% confidence interval for the mean number of hours statistics students will spend watching television in one week.

Table$8.4$

Construct a $90\%$ confidence interval for the population mean time to complete the forms. State the confidence interval, sketch the graph and calculate the error bound.

Fill in the blanks on the graph with the areas, upper and lower limits of the confidence interval, and the sample

proportion.

Using the same p′ and level of confidence, suppose that n were increased to 100. Would the error bound become larger

or smaller? How do you know?

If you decreased the allowable error bound, why would the minimum sample size increase (keeping the same level of

confidence)?

Among various ethnic groups, the standard deviation of heights is known to be approximately three inches. We wish

to construct a 95% confidence interval for the mean height of male Swedes. Forty-eight male Swedes are surveyed. The

sample mean is 71 inches. The sample standard deviation is 2.8 inches.

a.

I. $\overline{X}$=________

ii. σ =________

iii. n =________

b. In words, define the random variables X and X

c. Which distribution should you use for this problem? Explain your choice.

d. Construct a 95% confidence interval for the population mean height of male Swedes.

I. State the confidence interval.

ii. Sketch the graph.

iii. Calculate the error bound.

e. What will happen to the level of confidence obtained if 1,000 male Swedes are surveyed instead of 48? Why?

Announcements for 84 upcoming engineering conferences were randomly picked from a stack of IEEE Spectrum

magazines. The mean length of the conferences was 3.94 days, with a standard deviation of 1.28 days. Assume the

underlying population is normal.

a. In words, define the random variables X and $\overline{X}$

b. Which distribution should you use for this problem? Explain your choice.

c. Construct a 95% confidence interval for the population mean length of engineering conferences.

I. State the confidence interval.

ii. Sketch the graph.

iii. Calculate the error bound.