Statistics_Test 4 (Chapters 8, 10, and 12)

The lifetime of a certain type of battery is known to be normally distributed with a poppulation standard deviation of 20 hours. A sample of 50 batteries had a mean lifetime of 120.1 hours. It is desired to construct a 99% confidence interval for the mean lifetime of this type of battery.

What is the Confidence Interval to one decimal place?

• (114.5, 125.6)

• (112.8, 127.4)

• (112.82, 127.38)

• (114.56, 125.64)

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CCSS.HSS.IC.B.4

An IQ test was given to a simple random sample of 75 students at a certain college. The sample mean score was 105.2. Scores on this test are known to have a population standard deviation of 10. It is desired to construct a 90% confidence interval for the mean IQ scores of the students at the college.

Find the Standard Error.

• 75

• 10

• 105.2

• 1.155

In a crash test of 15 troopers, collision repair costs are found to have a distribution that is approximately normal, with a mean of $1800 and a standard deviation of $950. Construct a 99% confidence interval for the repair cost for the population.

• (1070, 2530)

• (1273, 2326)

• (1799, 1801)

• (1776, 1823)

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CCSS.HSS.IC.B.4

A research group wishes to estimate the mean amount of time (in hours) that members of a fitness center spend exercising each week. They want to estimate the mean within a margin of error of 0.5 hours with a 95% level of confidence. Previous data suggests that the standard deviation of the population is 2.2. Which of the following is the smallest sample size they could use?

• 60

• 75

• 90

• 180

Thirty randomly selected students took the calculus final. If the sample mean was 92 and the standard deviation was 9.4, construct a 99 percent confidence interval for the mean score of all students from which the sample was gathered.

• 87.27 < μ < 96.73

• 89.08 < μ < 94.92

• 87.29 < μ < 96.71

• 87.77 < μ < 96.23

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CCSS.HSS.IC.B.4

The weight of the average 6th grade student's backpack (with books in it) is 18.4 lbs. The principal of the school thinks that the backpack does not weight 18.4 lbs. What is the null and alternate hypothesis? 

• H₀ = 18.4
  H_a = 18.4
• H₀ = 18.4
  H_a > 18.4
• H₀ = 18.4
  H_a < 18.4
• H₀ = 18.4
  H_a ≠ 18.4

When do you use a t-test instead of a z-test?

• When the population standard deviation is not known.

• When the population standard deviation is given.

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CCSS.HSS.ID.A.4

The average miles on a tank of gas for the Ford

Explorer is 300 miles with a standard deviation of 22

miles. A consumer group feels the average is actually

lower. They survey 39 vehicles and find the average

miles per tank is 290 miles. At α = 0.05, test the

consumer groups’ claim that the miles per tank is

actually lower than 300 miles.

• Reject Ho

• Reject Ha

• Fail to reject Ho

• Fail to reject Ha

A fast food outlet claims that the mean waiting time in

line is less than 3.5 minutes. A random sample of 20

customers has a mean of 3.7 minutes with a standard

deviation of 0.8 minute. If α = 0.05, test the fast food

outlet's claim.

• Reject Ho

• Reject Ha

• Fail to reject Ho

• Fail to reject Ha

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CCSS.HSS.ID.A.4

Given the following information, find the z-value for the sample. (Hint: z = (x-bar - μ)/(σ/√n))

x-bar = 71, μ = 68, σ = 7.5, n = 36

• 2.40

• 3.00

• 2.78

• 6.90

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CCSS.HSS.ID.A.4