Question

# 9.) How many commuters must be randomly selected to estimate the mean driving time of Chicago...

9.) How many commuters must be randomly selected to estimate the mean driving time of Chicago commuters? We want 95% confidence that the sample mean is within 3 minutes of the population mean, and the population standard deviation is known to be 12 minutes.

A. 61 commuters

B. 8 commuters

C. 62 commuters

D. 7 commuters

10.) If we increase our sample size the width of the confidence interval will

A. increase

B. stay the same

C. decrease

11.) Data collected by child development scientists produced the following 90% confidence interval for the average age (in months) at which children say their first word: (10.1 months, 13.4 months). Which statement correctly interprets this interval?

A. Based on this sample, we can say, with 90% confidence, that the mean age at which children say their first word is between 10.1 and 13.4 months.

B. 90% of the children in this sample said their first word when they were between 10.1 and 13.4 months old.

C. If we took many random samples of children, about 90% of them would produce this confidence interval.

D. We are 90% sure that a child will say his first word when he is between 10.1 and 13.4 months old.

9)

Solution :

Given that,

standard deviation = = 12

margin of error = E = 3

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96

Sample size = n = ((Z/2 * ) / E)2

= ((1.96 * 12) / 3)2

= 61.46 = 62

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