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Exam 11: Inferences About Population Variances

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Question 31

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To avoid the problem of not having access to tables of the F distribution with values given for the lower tail when a two-tailed test is required, let the smaller sample variance be _____.

A) the denominator of the test statistic
B) the numerator of the test statistic
C) at least 1
D) None of the answers is correct.

E) B) and C)
F) None of the above

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Question 32

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A sample of 61 items provided a sample mean of 932, a sample mode of 900, and a sample standard deviation of 11. Test the following hypotheses using α = .05. What is your conclusion? ​ H₀: α² ≤ 80 H_a: α² > 80

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χ² = 90.75 > 83.2976; reject H₀,...

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Question 33

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In Excel, which of the following functions is used to conduct a hypothesis test (using the p-value) for a population variance?

A sample of 20 cans of tomato juice showed a standard deviation of 0.4 ounce. A 95% confidence interval estimate of the variance for the population is _____.

To avoid the problem of not having access to tables of F distribution with values given for the lower tail, the numerator of the test statistic should be the one with the _____.

The sampling distribution of the $\frac { ( n - 1 ) s ^ { 2 } } { \sigma ^ { 2 } }$ quantity is the _____.

The data below shows samples of annual salaries (in $1000s) for accountants in two different firms. $\begin{array}{l}\text { Company A}&\text { Company B }\\74.8 & 83.3 \\78.2 & 65.7 \\69.9 & 82.1 \\84 & 78.5 \\65.7 & 69.7 \\66.8 & 77.7 \\72.1 & 66.7 \\77.4 & 78.4 \\79.3 & 79.2 \\69.1 & 80.1 \\& 74.9 \\& 69.8\end{array}$ Use Excel to determine whether the variance in salaries in Company A differs from that of Company B. Use a .10 level of significance.

The 99% confidence interval estimate for a population variance when a sample standard deviation of 12 is obtained from a sample of 10 items is _____.

The sampling distribution of the ratio of independent sample variances extracted from two normal populations with equal variances is the _____.

At α = .1, test to see if the population variances from which the following samples were drawn are equal. Group $1 \quad$ Group 2 $\begin{array} { l l } n _ { 1 } = 21 & n _ { 2 } = 19 \\s _ { 1 } = 18 & s _ { 2 } = 16\end{array}$ ​

A sample of 30 items provided a sample mean of 28 and a sample standard deviation of 6. Test the following hypotheses using α = .05. What is your conclusion? ​ H₀: σ² ≤ 25 H_a: σ² > 25

Do the following data indicate that the variance of the population from which this sample has been drawn is significantly more than 12? Use α = .05. $\begin{array} { l l l l l l } 16 & 12 & 21 & 10 & 13 & 18\end{array}$

The specifications for the filling of soft drink bottles is a variance of .05 (ounces)². A sample of 20 bottles of soft drink showed the following results: $\begin{array} { l l l l l } 12.03 & 12.01 & 11.89 & 12.15 & 12.23 \\11.97 & 12.10 & 11.85 & 12.33 & 12.02 \\11.96 & 12.00 & 11.82 & 12.02 & 11.99 \\11.96 & 11.83 & 11.84 & 12.21 & 12.38\end{array}$ At a 5% level of significance, use Excel to determine whether or not the variance of the population is significantly different from .05.

A lumber company has claimed that the standard deviation for the lengths of its six-foot boards is 0.5 inch or less. To test its claim, a random sample of 17 six-foot boards is selected, and it is determined that the standard deviation of the sample is .43. Do the results of the sample support the company's claim? Use α = .1.

The symbol used for the variance of the sample is _____.

The χ² value for a one-tailed test (lower tail) when the level of significance is .1 and the sample size is 15 is _____.

The 90% confidence interval estimate for a population standard deviation when a sample variance of 50 is obtained from a sample of 15 items is _____.

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

A sample of 16 students showed that the variance in the number of hours they spend studying is 25. At a 5% level of significance, test to see if the variance of the population is significantly different from 30.

A sample of 28 elements is selected to estimate a 95% confidence interval for the variance of the population. The χ² values to be used for this interval estimation are _____.