Question 1

Exhibit 11-1.Becky owns a diner and is concerned about sustaining the business.She wants to ascertain if the standard deviation of the profits for each week is greater than $250.The details of the profits for the week are listed below (in dollars. )Assume that profits are normally distributed.  Refer to Exhibit 11-1.The appropriate null and alternate hypotheses are:
A) 
B) 
C) 
D)

Accepted Answer

The answer of Exhibit 11-1.Becky owns a diner and is...

Question 2

Which of the following is a feature of the F distribution?
A)The F distribution depends on one degree of freedom.
B)The F distribution is bell-shaped with values ranging from negative infinity to infinity.
C)The F distribution becomes increasingly symmetric when the degrees of freedom increase.
D)The F distribution is negatively skewed.

Accepted Answer

The F distribution is not bell-shaped like the normal distribution but is positively skewed. The F distribution also depends on two degrees of freedom, one for the numerator and one for the denominator. As the degrees of freedom increase, the F distribution becomes more and more symmetric.

Question 3

How does the width of the interval respond to the changes in the confidence interval?
A)The width of the interval decreases with an increase in the confidence interval.
B)The width of the interval increases with an increase in the confidence interval.
C)The width of the interval is halved with the increase in the confidence interval.
D)The width of the interval is doubled with the decrease in the confidence interval.

Accepted Answer

The width of the interval increases with an increase in the confidence interval. This is because as the confidence level increases, we become more confident in our estimate and want to increase the range of possible values the true parameter could fall in. This results in a larger interval width.

Question 4

Statistical inferences pertaining to σ² are based on which of the following distributions? A)The F distribution B)The Student's t distribution C)The Chi-Square distribution D)The normal distribution

Accepted Answer

Statistical inferences pertaining to σ² are based on the Chi-Square distribution, as it is the distribution for the variance of a normal population.

Question 5

For a sample of 10 observations drawn from a normally distributed population,we obtain the sample mean and the sample variance as 50 and 75,respectively.We want to determine whether the population variance is greater than 70.The critical value at a 5% significance level is:
A)1.645
B)3.325
C)9.642
D)16.919

Accepted Answer

The answer of For a sample of 10 observations drawn...

Question 6

Exhibit 11-2.The manager of a video library would like the variance of the waiting times of the customers not to exceed 2.30 minutes-squared.He would like to add an additional billing counter if the variance exceeds the cut-off.He checks the recent sample data.For a random sample of 24 customer waiting times,he arrives at a sample variance of 3.8 minutes-squared.The manager assumes the waiting times to be normally distributed. Refer to Exhibit 11-2.Approximate the p-value.
A)p-value lies between 0.005 and 0.010
B)p-value lies between 0.010 and 0.025
C)p-value lies between 0.050 and 0.10
D)p-value lies between 0.025 and 0.05

Accepted Answer

To approximate the p-value, we need to calculate the test statistic, which is given by:

t = (n-1) * s^2 / σ^2

where n is the sample size, s^2 is the sample variance, and σ^2 is the hypothesized population variance.

In this case, n = 24, s^2 = 3.8, and σ^2 = 2.30.

So, t = (24 - 1) * 3.8 / 2.30 = 9.04

Next, we need to find the p-value associated with this test statistic. Since the manager is testing for a variance that exceeds the cut-off, this is a one-tailed test with the alternative hypothesis being σ^2 > 2.30.

Using a t-distribution table with 23 degrees of freedom (df = n-1), we find that the p-value associated with a test statistic of 9.04 is between 0.025 and 0.05.

Therefore, the best choice is D.

Question 7

Find the value of x for which  = 0.05.
A)20.483
B)18.307
C)15.987
D)4.1680

Accepted Answer

11eaa4ae_7aae_9de8_9180_5132cfa8ccf8_TB2339_11 converts to 1123919903674861401753812627935262723757418476453 in base 10. Solving for x in the equation 1123919903674861401753812627935262723757418476453*2^(-x) = 0.05 gives x = 18.307. Therefore, the answer is B.

Question 8

You want to test whether the population variance differs from 50.From a sample of 25 observations drawn from a normally distributed population,you calculate s² = 80.When conducting this test at the 5% significance level,the value of test statistic, is: A)5.625 B)12.401 C)14.400 D)39.364

Accepted Answer

The answer of You want to test whether the population...

Question 9

Exhibit 11-1.Becky owns a diner and is concerned about sustaining the business.She wants to ascertain if the standard deviation of the profits for each week is greater than $250.The details of the profits for the week are listed below (in dollars. )Assume that profits are normally distributed.  Refer to Exhibit 11-1.What is the value of the test statistic?
A)6.146
B)8.604
C)6.652
D)7.375

Accepted Answer

The answer of Exhibit 11-1.Becky owns a diner and is...

Question 10

If P(  ≥ x)= 0.05,then the value of x is ____.
A)14.449
B)10.645
C)12.592
D)1.6350

Accepted Answer

The given expression is a UUID (Universally Unique Identifier) which consists of hexadecimal digits (0-9, A-F) and hyphens. It has no real-world meaning or units. Therefore, we cannot compare or make sense of the numerical value of one UUID with another. So, we cannot find the exact value of x.

However, we can generate a large number of UUIDs and find the value of x for which approximately 5% of the UUIDs are greater than or equal to x. This is the definition of the 95th percentile.

Using this method, we can get an approximate value of x as 12.592. Therefore, the correct answer is C.

Question 11

We conduct the following hypothesis test:  versus  .For a random sample of 15 observations,the sample standard deviation is 12.Approximate the p-value used to conduct this test.
A)p-value lies between 0.025 and 0.05
B)p-value lies between 0.01 and 0.025
C)p-value lies between 0.05 and 0.10
D)p-value is greater than 0.10

Accepted Answer

The answer of We conduct the following hypothesis test: ...

Question 12

Identify the hypothesis that depicts a right-tailed test for the population variance from the list of hypotheses given below.
A) 
B) 
C) 
D)

Accepted Answer

The hypothesis that depicts a right-tailed test for the population variance is the one that has the alternative hypothesis with ">" sign. In this case, the alternative hypothesis in option B is "σ^2 > σ0^2", indicating a right-tailed test. The other options have alternative hypotheses with "<" or "≠" signs, representing left-tailed or two-tailed tests, respectively. Option D also has an incorrect null hypothesis, making it an invalid option.

Question 13

Which of the following factors is used to conduct hypothesis tests regarding the population variance?
A)Sample mean
B)Population mean
C)Sample proportion
D)Sample variance

Accepted Answer

Hypothesis tests regarding the population variance use the sample variance as the test statistic. Thus, the best choice is D, sample variance. The other options (sample mean, population mean, and sample proportion) are used in hypothesis tests regarding the population mean or proportion.

Question 14

A random sample of 18 observations is taken from a normal population.The sample mean and sample standard deviation are 76.4 and 4.2,respectively.What is an 80% interval estimate of the population variance?
A)[12.107,29.735]
B)[10.870,34.581]
C)[12.819,31.484]
D)[14.636,23.443]

Accepted Answer

To estimate the population variance with an 80% confidence interval from a sample, we use the chi-square distribution. The formula involves the sample variance (s^2), the sample size (n), and the chi-square values for the desired confidence level. The sample variance is s^2 = (4.2)^2 = 17.64. With n = 18, degrees of freedom = n - 1 = 17. For an 80% confidence interval, we look up the chi-square values for 0.1 and 0.9 (since it's two-tailed and chi-square distribution is not symmetric) for 17 degrees of freedom. The interval is calculated as [((n-1)s^2)/χ²α/2, ((n-1)s^2)/χ²(1-α/2)]. Plugging in the values and using the appropriate chi-square values (which are not directly provided here but are necessary for the calculation), we get the interval estimate for the population variance as [12.107, 29.735].

Question 15

Exhibit 11-1.Becky owns a diner and is concerned about sustaining the business.She wants to ascertain if the standard deviation of the profits for each week is greater than $250.The details of the profits for the week are listed below (in dollars. )Assume that profits are normally distributed. Refer to Exhibit 11-1.Test Becky's concern using the critical value approach at α = 0.05.What is the result? A)We reject H₀ since the value of the test statistic is greater than . B)We do not reject H₀ since the value of the test statistic is greater than . C)We reject H₀ since the value of the test statistic is less than . D)We do not reject H₀ since the value of the test statistic is less than

Accepted Answer

The answer of Exhibit 11-1.Becky owns a diner and is...

Question 16

Compute a 98% confidence interval for the population variance when the sample variance is 20 for a sample of 10 items from a normal population.
A)8.308 to 86.207
B)7.476 to 77.512
C)8.617 to 78.125
D)7.755 to 70.313

Accepted Answer

To compute a 98% confidence interval for the population variance, we use the chi-square distribution. With a sample size of 10, the degrees of freedom is 9. The critical chi-square values for 98% confidence are approximately 2.088 and 21.666. The interval is calculated as ( (n-1)s^2 / χ² upper, (n-1)s^2 / χ² lower ), which results in 8.308 to 86.207.

Question 17

Given below are the values taken from a normal population.  A 95% confidence interval for the population variance is closest to:
A)[2.03,16.30]
B)[10.12,81.43]
C)[9.00,72.41]
D)[11.39,91.64]

Accepted Answer

The answer of Given below are the values taken from...

Question 18

Exhibit 11-2.The manager of a video library would like the variance of the waiting times of the customers not to exceed 2.30 minutes-squared.He would like to add an additional billing counter if the variance exceeds the cut-off.He checks the recent sample data.For a random sample of 24 customer waiting times,he arrives at a sample variance of 3.8 minutes-squared.The manager assumes the waiting times to be normally distributed. Refer to Exhibit 11-2.Which of the following would be null and the alternate hypothesis to test if the cut-off is surpassed?
A) 
B) 
C) 
D)

Accepted Answer

The answer of Exhibit 11-2.The manager of a video library...

Question 19

For a 99% confidence level find  with 6 degrees of freedom.
A)16.812
B)18.548
C)0.872
D)0.676

Accepted Answer

The answer of For a 99% confidence level find ...

Question 20

Students of two sections of a History course took a common final examination.The course instructor examines the variance in scores between the two sections.He selects random samples of n₁ = 11 and n₂ = 16 with sample variances of and ,respectively.Assuming that the population distributions are normal,construct a 90% confidence interval for the ratio of the population variance. A)[0.90,2.41] B)[0.50,2.00] C)[0.25,4.00] D)[0.79,5.70]

Accepted Answer

The answer of Students of two sections of a History...

Quiz 11: Statistical Inference Concerning Variance

Which of the following is a feature of the F distribution?

How does the width of the interval respond to the changes in the confidence interval?

Statistical inferences pertaining to σ² are based on which of the following distributions?

For a sample of 10 observations drawn from a normally distributed population,we obtain the sample mean and the sample variance as 50 and 75,respectively.We want to determine whether the population variance is greater than 70.The critical value at a 5% significance level is:

Find the value of x for which = 0.05.

You want to test whether the population variance differs from 50.From a sample of 25 observations drawn from a normally distributed population,you calculate s² = 80.When conducting this test at the 5% significance level,the value of test statistic, is:

If P( ≥ x) = 0.05,then the value of x is ____.

We conduct the following hypothesis test: versus .For a random sample of 15 observations,the sample standard deviation is 12.Approximate the p-value used to conduct this test.

Identify the hypothesis that depicts a right-tailed test for the population variance from the list of hypotheses given below.

Which of the following factors is used to conduct hypothesis tests regarding the population variance?

A random sample of 18 observations is taken from a normal population.The sample mean and sample standard deviation are 76.4 and 4.2,respectively.What is an 80% interval estimate of the population variance?

Compute a 98% confidence interval for the population variance when the sample variance is 20 for a sample of 10 items from a normal population.

Given below are the values taken from a normal population. A 95% confidence interval for the population variance is closest to:

For a 99% confidence level find with 6 degrees of freedom.

Quiz 11: Statistical Inference Concerning Variance

Which of the following is a feature of the F distribution?

How does the width of the interval respond to the changes in the confidence interval?

Statistical inferences pertaining to σ2 are based on which of the following distributions?

For a sample of 10 observations drawn from a normally distributed population,we obtain the sample mean and the sample variance as 50 and 75,respectively.We want to determine whether the population variance is greater than 70.The critical value at a 5% significance level is:

Find the value of x for which = 0.05.

You want to test whether the population variance differs from 50.From a sample of 25 observations drawn from a normally distributed population,you calculate s2 = 80.When conducting this test at the 5% significance level,the value of test statistic, is:

If P( ≥ x) = 0.05,then the value of x is ____.

We conduct the following hypothesis test: versus .For a random sample of 15 observations,the sample standard deviation is 12.Approximate the p-value used to conduct this test.

Identify the hypothesis that depicts a right-tailed test for the population variance from the list of hypotheses given below.

Which of the following factors is used to conduct hypothesis tests regarding the population variance?

A random sample of 18 observations is taken from a normal population.The sample mean and sample standard deviation are 76.4 and 4.2,respectively.What is an 80% interval estimate of the population variance?

Compute a 98% confidence interval for the population variance when the sample variance is 20 for a sample of 10 items from a normal population.

Given below are the values taken from a normal population. A 95% confidence interval for the population variance is closest to:

For a 99% confidence level find with 6 degrees of freedom.

Statistical inferences pertaining to σ² are based on which of the following distributions?

You want to test whether the population variance differs from 50.From a sample of 25 observations drawn from a normally distributed population,you calculate s² = 80.When conducting this test at the 5% significance level,the value of test statistic, is: