# Solved > 31.True or False: The t distribution is used:1754013 …

31.True or False: The t distribution is used to develop a confidence interval estimate of the population mean when the population standard deviation is unknown.

32.True or False:  For a t distribution with 12 degrees of freedom, the area between – 2.6810 and

2.1788 is 0.980.

33.If you were constructing a 99% confidence interval of the population mean based on a sample of n=25 where the standard deviation of the sample S = 0.05, the critical value of t will be a) 2.7969

b)2.7874

c)2.4922

d)2.4851

34.Which of the following is not true about the Student’s t distribution?

a)It has more area in the tails and less in the center than does the normal distribution.

b)It is used to construct confidence intervals for the population mean when the population standard deviation is known.

c)It is bell shaped and symmetrical.

d)As the number of degrees of freedom increases, the t distribution approaches the normal distribution.

35.True or False:  The t distribution is used to construct confidence intervals for the population mean when the population standard deviation is unknown.

36.The t distribution

a)assumes the population is normally distributed.

b)approaches the normal distribution as the sample size increases.

c)has more area in the tails than does the normal distribution.

d)All of the above.

37.It is desired to estimate the mean total compensation of CEOs in the Service industry. Data were randomly collected from 18 CEOs and the 95% confidence interval was calculated to be (\$2,181,260, \$5,836,180). Which of the following interpretations is correct?

a)95% of the sampled total compensation values fell between \$2,181,260 and \$5,836,180.

b)We are 95% confident that the mean of the sampled CEOs falls in the interval \$2,181,260 to \$5,836,180.

c)In the population of Service industry CEOs, 95% of them will have total compensations that fall in the interval \$2,181,260 to \$5,836,180.

d)We are 95% confident that the mean total compensation of all CEOs in the Service industry falls in the interval \$2,181,260 to \$5,836,180.

38.It is desired to estimate the mean total compensation of CEOs in the Service industry. Data were randomly collected from 18 CEOs and the 95% confidence interval was calculated to be (\$2,181,260, \$5,836,180). Based on the interval above, do you believe the mean total compensation of CEOs in the Service industry is more than \$3,000,000?

a)Yes, and I am 95% confident of it.

b)Yes, and I am 78% confident of it.

c)I am 95% confident that the mean compensation is \$3,000,000.

d)I cannot conclude that the mean exceeds \$3,000,000 at the 95% confidence level.

39.Suppose a 95% confidence interval for μ turns out to be (1,000, 2,100). Give a definition of what it means to be “95% confident” as an inference.

a)In repeated sampling, the population parameter would fall in the given interval 95% of the time.

b)In repeated sampling, 95% of the intervals constructed would contain the population mean.

c)95% of the observations in the entire population fall in the given interval.

d)95% of the observations in the sample fall in the given interval.

40.A major department store chain is interested in estimating the mean amount its credit card customers spent on their first visit to the chain’s new store in the mall. Fifteen credit card

accounts were randomly sampled and analyzed with the following results: X = \$50.50 and

S = 20 . Assuming the distribution of the amount spent on their first visit is normal, what is the shape of the sampling distribution of the sample mean that will be used to create the desired confidence interval for μ?

a)Approximately normal with a mean of \$50.50

b)A standard normal distribution

c)A t distribution with 15 degrees of freedom

d)A t distribution with 14 degrees of freedom

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