1) A national beauty salon chain wants to estimate the number of times per year a woman has her hair done at a beauty salon if she uses one at least once a year. The chain's researcher estimates that, of those women who use a beauty salon at least once a year, the standard deviation of number of times of usage is approximately seven. The national chain wants the estimate to be within three times of the actual mean value. How large a sample should the researcher take to obtain a 90% confidence interval?

Round thez-value to 3 decimal places and round the sample size up to the nearest whole number.

For part (a), use a positivez-value.

(a) What is the criticalz-value that will need to be used to calculate the sample size?

For part (b), round your answer UP to the nearest whole number.

(b) What is the sample size required?

2)In a time-use study, 75 randomly selected managers were found to spend a mean of 2.97 h each day on paperwork. The population standard deviation is known to be about 1.15 h. Construct the 95 % confidence interval for the mean time spent on paperwork by all managers.

Round thez-value to 3 decimal places and the confidence interval values to 2 decimal places.

For part (a), use a positivez-value.

(a) What is the criticalz-value that will need to be used to calculate the confidence interval?

(b) What is the 95% confidence interval?

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3) Suppose a business researcher wants to estimate the average travel time to work in Etobicoke using a 98% level of confidence. A random sample 226 Toronto commuters is taken and the travel time to work is obtained from each. The sample mean is 51.1 minutes, and the population standard deviation is estimated to be about 18.0 minutes. Compute a 98% confidence interval on the data. (Use the z-distribution.)

Round thez-value to 3 decimal places and the confidence interval values to 1 decimal place.

For part (a), use a positivez-value.

(a) What is the criticalz-value that will need to be used to calculate the confidence interval?

(b) What is the 98% confidence interval?

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