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Exam 11: Inferences About Population Variances

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Question 31

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Consider the following hypothesis problem. n = 23, s2 = 60, H₀: σ² ≥ 66, H_a: σ² < 66 If the test is to be performed at the 5% level, what are the critical value(s) from the chi-square distribution?

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Question 32

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​In practice, the most frequently encountered hypothesis test about a population variance is a

A) ​one-tailed test, with rejection region in the lower tail.
B) ​one-tailed test, with rejection region in the upper tail.
C) ​two-tailed test, with equal-size rejection regions.
D) ​two-tailed test, with unequal-size rejection regions.

E) None of the above
F) All of the above

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Question 33

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A sample of 51 observations yielded a sample standard deviation of 5.If we want to test H₀: σ² = 20, the test statistic is

The random variable for a chi-square distribution may assume

At α = .1, test to see if the population variances from which the following samples were drawn are equal.

A sample of 60 items from population 1 has a sample variance of 12 while a sample of 50 items from population 2 has a sample variance of 15.If we want to test whether the variances of the two populations are equal, the test statistic will have a value of

The standard deviation of the ages of a sample of 16 executives from the northern states was 8.2 years; while the standard deviation of the ages of a sample of 25 executives from the southern states was 12.8 years.At α = .1, test to see if there is any difference between the variances of the ages of all the northern and all the southern executives.

A random sample of 31 sales charge showed a sample standard deviation of $50.What is the 90% confidence interval estimate of the population standard deviation?

​Consider the following sample information from Population A and Population B. ​ ​ Sample A Sample B N 24 16 S² 32 38 ​​ We want to test the hypothesis that the population variances are equal.The test statistic for this problem equals

A lumber company has claimed that the standard deviation for the lengths of their six-foot boards is .4 inches or less.To test their claim, a random sample of 16 six-foot boards is selected; and it is determined that the variance of the sample is .3.Do the results of the sample support the company's claim? Use α = .1.

The value of F_.05 with 8 numerator and 19 denominator degrees of freedom is

​Consider the following hypothesis problem. n = 14 H₀: σ² < 410 S = 20 H_a: σ² > 410 ​ ​The test statistic equals

The value of F_.01 with 9 numerator and 20 denominator degrees of freedom is

A company claims that the standard deviation in their delivery times is less than 5 days.A sample of 27 past customers was taken.The average delivery time in the sample was 14 days with a standard deviation of 4.5 days.At the 5% level of significance, test the company's claim.Use the critical value approach.

?Which of the following rejection rules is proper?

Student advisors are interested in determining if the variances of the scores of day students and night students are the same.The following samples are drawn: Day Night n₁ = 25 n₂ = 31 s₁ = 9.8 s₂ = 14.7 ​ Test the equality of the variances of the populations.Let α = .05.

​Consider the following hypothesis problem. n = 14 H₀: σ² < 410 S = 20 H_a: σ² > 410 ​ ​The null hypothesis is to be tested at the 5% level of significance.The critical value(s) from the chi-square distribution table is(are)

A random sample of 21 checking accounts at a bank showed an average daily balance of $430 with a standard deviation of $50. a. Provide a 95% confidence interval estimate for the variance of the population of the checking accounts. b. Provide a 95% confidence interval estimate for the standard deviation of the population of the checking accounts.

Which of the following has a chi-square distribution?

A sample of n observations is taken from a normal population.The appropriate chi-square distribution has