Review Ch 6 and 7 (answers at the bottom)
1) A random sample of 40 students has a mean annual earnings of $3120 and a standard deviation of
$677. Construct the confidence interval for the population mean, µ if c = 0.95.
A) ($4812, $5342) B) ($2910, $3330)
C) ($1987, $2346) D) ($210, $110)
2) In a sample of 10 randomly selected women, it was found that their mean height was 63.4 inches.
From previous studies, it is assumed that the standard deviation, sigma, is 2.4. Construct the 95%
confidence interval for the population mean. Assume the population is normally distributed.
A) (58.1, 67.3) B) (60.8, 65.4) C) (59.7, 66.5) D) (61.9, 64.9)
3) A nurse at a local hospital is interested in estimating the birth weight of infants. How large a sample
must she select if she desires to be 99% confident that the true mean is within 3 ounces of the sample
mean? The standard deviation of the birth weights is known to be 8 ounces.
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4) (same as previous problem with different #s) A nurse at a local hospital is interested in estimating the
birth weight of infants. How large a sample must she select if she desires to be 99% confident that the
true mean is within 4 ounces of the sample mean? The standard deviation of the birth weights is known to
be 9 ounces.
A) 33 B) 5 C) 34 D) 6
5) Construct a 99% confidence interval for the population mean, µ. Assume the population has a normal
distribution. A group of 19 randomly selected students has a mean age of 22.4 years with a standard
deviation of 3.8 years.
A) (18.7, 24.1) B) (16.3, 26.9) C) (19.9, 24.9) D) (17.2, 23.6)
6) (Sec 6.3 – omit su06) A survey of 250 households showed 62 owned at least one gun. Construct a
90% confidence interval for the proportion of households that own at least one gun.
A) (0.369, 0.451) B) (0.683, 0.712)
C) (0.103, 0.189) D) (0.203, 0.293)
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7) A candidate for governor of a particular state claims to be favored by at least half of the voters. Write
the claim first. Then write the null and alternative hypotheses.
8) The mean IQ of statistics teachers is greater than 140. State this claim mathematically. Write the null
and alternative hypotheses.
9) Test the claim that µ= 1050, given that alpha = 0.01 and the sample statistics are n = 35,
x = 1020, and s = 82.
10) A trucking firm suspects that the mean lifetime of a certain tire it uses is less than 35,000 miles. To
check the claim, the firm randomly selects and tests 54 of these tires and gets a mean lifetime of 34,650
miles with a standard deviation of 1200 miles. At α = 0.05, test the trucking firm's claim.
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11) Find the standardized test statistic t for a sample with n = 15, x = 3.1, s = 0.8, and α = 0.05 if Ho: μ
≤ 2.8. Round your answer to three decimal places. Assume the population is normally distributed.
A) 1.452 B) 1.631 C) 1.312 D) 1.728
12) (another trucking problem with diff. #s) A trucking firm suspects that the mean life of a certain tire it
uses is less than 39,000 miles. To check the claim, the firm randomly selects and tests 18 of these tires
and gets a mean lifetime of 38,300 miles with a standard deviation of 1200 miles. At α = 0.05, test the
trucking firm's claim. Assume the population is normally distributed.
Answers:
1) B
2) D (z-int)
3) 48
4) C
5) C (t-int)
6) D
7) claim: p > .5; H0: p > 0.5, Ha: p < 0.5 claim is Ho
8) claim: mu > 140; H0: mu < 140, Ha: mu > 140; claim is Ha
9) claim: mu = 1050;
H0: mu =1050, Ha: mu ≠ 1050; claim is H0
- standardized test statistic -2.16, critical value z = +2.575 and -2.575, fail to reject H0.
There is not enough evidence to reject the claim that the mean is1050.
10) claim: mu < 35000; H0: mu > 35000, Ha: mu < 35000; claim is Ha ;
- standardized test statistic -2.14; critical value t = -1.645; reject H0; There is sufficient evidence to
support the trucking firm's claim.
11) A
12) claim: mu < 39000; H0: mu > 39000; Ha: mu < 39000; claim is Ha;
test statistic -2.47; critical value t = -1.740; reject H0; There is sufficient evidence to support the
trucking firm's claim.
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