Question 1

A mail-order business prides itself in its ability to fill customers' orders in less than six calendar days, on average. Periodically, the operations manager selects a random sample of customer orders and determines the number of days required to fill the orders. On one occasion when a sample of 30 orders was selected, the average number of days was 6.65 with a sample standard deviation of 1.5 days. Assume the time in which an order is filled is normally distributed.

-What is the critical value to test the hypotheses at ? = .10.
A)-1.282
B)-1.96
C)-1.311
D)1.282
E)1.311

Accepted Answer

The critical value for a one-tailed test at a significance level of 0.10 with 29 degrees of freedom (n-1) is approximately -1.311.

Question 2

Suppose we are comparing two population means from normally distributed populations based on independent random samples and unknown,but equal,population variances.If n₁ = 13 and n₂ = 10,then degrees of freedom for the t statistic is 22.

Accepted Answer

The degrees of freedom for the t statistic in this case is calculated using the formula for pooled variance, which results in $df = n_1 + n_2 - 2$. Given $n_1 = 13$ and $n_2 = 10$, the degrees of freedom $df = 13 + 10 - 2 = 21$.

Question 3

In the past, the average waiting time per customer at a fast food restaurant has been 7.5 minutes. The customer waiting time has a normal distribution. The manager claims that the use of a new cashier system will decrease the average customer waiting time in the store. A random sample of 16 customer transactions produces a mean waiting time of 6.3 minutes and a standard deviation of 2 minutes. -At the 5% level of significance,how would we define the rejection region? A)z < -1.645 B)z > 1.645 C)t > 1.753 D)t < -1.753 E)t < -1.782

Accepted Answer

Given that the sample size is small (n=16) and the population standard deviation is unknown, a t-test is appropriate for testing the manager's claim. The rejection region for a left-tailed test at the 5% significance level with 15 degrees of freedom (n-1) is t < -1.753.

Question 4

A mail-order business prides itself in its ability to fill customers' orders in less than six calendar days, on average. Periodically, the operations manager selects a random sample of customer orders and determines the number of days required to fill the orders. On one occasion when a sample of 30 orders was selected, the average number of days was 6.65 with a sample standard deviation of 1.5 days. Assume the time in which an order is filled is normally distributed.

-Give a range for the p-value for this test.
A)0.01 < p-value < 0.025
B)0.001 < p-value < 0.005
C)0.005 < p-value < 0.01
D)0.05 < p-value < 0.10
E)0.025 < p-value < 0.05

Accepted Answer

The sample mean is 6.65 days, which is greater than the population mean of 6 days. Using a one-sample t-test to test if the true mean is greater than 6 days, given the sample size (30), mean (6.65), and standard deviation (1.5), the result is a p-value that is small because the sample mean is significantly higher than the population mean. However, without calculating the exact p-value, we can infer it's relatively small due to the significant difference and the sample size. Option A provides a reasonable range for such a scenario, indicating that the p-value is significant but not extremely so, suggesting that there is evidence against the null hypothesis that the mean is less than or equal to 6 days.

Question 5

The F distribution is skewed to the left.

Accepted Answer

The F distribution is actually skewed to the right.

Question 6

Suppose we are comparing the population variances of two normally distributed populations using independent random samples.If $s _ { 1 } ^ { 2 } = s _ { 2 } ^ { 2 }$ 
,the calculated value of the F statistic will always be equal to one.

Accepted Answer

The F statistic for comparing two variances is calculated as $F = \frac{s_1^2}{s_2^2}$. If $s_1^2 = s_2^2$, then $F = \frac{s_1^2}{s_2^2} = 1$.

Question 7

In testing the difference between population variances of two normally distributed populations using independent random samples,it is a common practice to compute the F statistic to assess if the value is greater than or equal to one.

Accepted Answer

This is true. The F statistic is calculated as the ratio of the sample variances, and is used to test the null hypothesis of equal variances in two populations. An F statistic greater than or equal to 1 suggests that the variance of one population is larger than the other, while an F statistic less than 1 suggests that the variances are similar. The F distribution is used to determine the probability of obtaining a particular F statistic, given the sample sizes and variances.

Question 8

A mail-order business prides itself in its ability to fill customers' orders in less than six calendar days, on average. Periodically, the operations manager selects a random sample of customer orders and determines the number of days required to fill the orders. On one occasion when a sample of 30 orders was selected, the average number of days was 6.65 with a sample standard deviation of 1.5 days. Assume the time in which an order is filled is normally distributed.

-Calculate the appropriate test statistic to test the hypotheses.
A)2.37
B)16.90
C)0.65
D)-2.37
E)3.31

Accepted Answer

The test statistic is calculated as (6.65 - 6) / (1.5 / sqrt(30)) = 2.37.

Question 9

In the past, the average waiting time per customer at a fast food restaurant has been 7.5 minutes. The customer waiting time has a normal distribution. The manager claims that the use of a new cashier system will decrease the average customer waiting time in the store. A random sample of 16 customer transactions produces a mean waiting time of 6.3 minutes and a standard deviation of 2 minutes.

-What is the value of the appropriate test statistic?
A)t = -1.2
B)t = 2.4
C)t = -2.4
D)t = -0.6
E)t = 9.6

Accepted Answer

The test statistic for a hypothesis test comparing sample means is calculated using the formula $t = \frac{\bar{x} - \mu}{(s/\sqrt{n})}$, where $\bar{x}$ is the sample mean, $\mu$ is the population mean, $s$ is the sample standard deviation, and $n$ is the sample size. Plugging in the given values: $t = \frac{6.3 - 7.5}{(2/\sqrt{16})} = \frac{-1.2}{0.5} = -2.4$.

Question 10

Suppose we are testing a null hypothesis about the population mean of a normally distributed population.If the population standard deviation is unknown and n = 14,the appropriate test statistic is based on the ___________ distribution.
A)t
B)z
C)F
D)chi-square
E)exponential

Accepted Answer

When the population standard deviation is unknown and the sample size is small (less than 30), we use the t-distribution to make inferences about the population mean. Therefore, the appropriate test statistic is based on the t-distribution.

Question 11

There are two types of machines called type A and type
B.Both type A and type B can be used to produce a certain product.The production manager wants to compare efficiency of the two machines.The manager assigns each of the 15 workers to both types of machines to compare the hourly production rate of the 15 workers.In other words,each worker operates machine A and machine B for one hour each.These two samples are independent.

Accepted Answer

The two samples are not independent because the same workers are operating both types of machines, creating a dependency between the two sets of data.

Question 12

In testing the difference between population variances of two normally distributed populations using independent random samples,the F statistic can assume either a positive or a negative value.

Accepted Answer

The F statistic can only assume a positive value because it is calculated as the ratio of two positive sample variances.

Question 13

A paired difference experiment is an experiment in which there is relationship between the measurements in the different samples.

Accepted Answer

In a paired difference experiment, the samples are related to each other as they involve measuring the same group of individuals or objects before and after an intervention or treatment. Therefore, there is a relationship between the measurements in the different samples.

Question 14

In a paired difference experiment,a sample of 12 pairs of observations is collected.The degree of freedom for the t statistic is 10.

Accepted Answer

The degrees of freedom for a paired difference experiment is calculated as the number of pairs minus one. Therefore, for 12 pairs, the degrees of freedom would be 12 - 1 = 11.

Question 15

A mail-order business prides itself in its ability to fill customers' orders in less than six calendar days, on average. Periodically, the operations manager selects a random sample of customer orders and determines the number of days required to fill the orders. On one occasion when a sample of 30 orders was selected, the average number of days was 6.65 with a sample standard deviation of 1.5 days. Assume the time in which an order is filled is normally distributed. -Set up the null and alternative hypotheses to test whether the standard is being violated. A)H₀: ? = 6 vs.H_a: ? ? 6 B)H₀: ? ? 6.65 vs.H_a: ? < 6.65 C)H₀: ? ? 6 vs.H_a: ? < 6 D)H₀: ? ? 6 vs.H_a: ? = 6 E)H₀: ? ? 6 vs.H_a: ? > 6

Accepted Answer

The null hypothesis (H0) is that the average time to fill orders is less than or equal to 6 days, which is the company's standard. The alternative hypothesis (Ha) is that the average time is greater than 6 days, indicating the standard is being violated. Option E correctly sets up these hypotheses.

Question 16

The F distribution is a symmetric distribution.

Accepted Answer

The F distribution is not a symmetric distribution. It is skewed to the right and has a peak at the left-hand side.

Question 17

When we are comparing the population means from two normally distributed populations based on independent random samples,the pooled estimate of the variance $s _ { p } ^ { 2 }$ 
is used if both population standard deviations are known.

Accepted Answer

The pooled estimate of the variance $s _ { p } ^ { 2 }$ is used when the population standard deviations are unknown but assumed to be equal. When both population standard deviations are known, there is no need to estimate variance using sample data.

Question 18

The F distribution is skewed to the right.

Accepted Answer

The F distribution is positively skewed (skewed to the right) because it has a long tail on the right side. This is due to the fact that the F distribution values are always positive and tend to be larger than 1.0.

Question 19

In the past, the average waiting time per customer at a fast food restaurant has been 7.5 minutes. The customer waiting time has a normal distribution. The manager claims that the use of a new cashier system will decrease the average customer waiting time in the store. A random sample of 16 customer transactions produces a mean waiting time of 6.3 minutes and a standard deviation of 2 minutes.
-Give a range for the p-value for this test.
A)0.01 < p-value < 0.025
B)0.001 < p-value < 0.005
C)0.005 < p-value < 0.01
D)0.05 < p-value < 0.10
E)0.025 < p-value < 0.05

Accepted Answer

The test statistic for this hypothesis test is calculated using the formula for a one-sample t-test, since the population standard deviation is not known. The formula is $t = \frac{\bar{x} - \mu}{(s/\sqrt{n})}$, where $\bar{x}$ is the sample mean, $\mu$ is the population mean, $s$ is the sample standard deviation, and $n$ is the sample size. Plugging in the given values, we get $t = \frac{6.3 - 7.5}{(2/\sqrt{16})} = \frac{-1.2}{0.5} = -2.4$. Looking up a t-value of -2.4 on the t-distribution table (or using software) for a one-tailed test with 15 degrees of freedom (since n-1 = 16-1 = 15), we find that the p-value falls between 0.01 and 0.025, indicating that there is statistical evidence to support the manager's claim at a significance level of less than 0.025 but more than 0.01.

Question 20

In testing the equality of population variances,two assumptions are required: independent samples and normally distributed populations.

Accepted Answer

Both assumptions of independent samples and normally distributed populations are necessary for testing the equality of population variances, as tests such as the F-test rely on these assumptions.

Quiz 8: Hypothesis Testing

Suppose we are comparing two population means from normally distributed populations based on independent random samples and unknown,but equal,population variances.If n1 = 13 and n2 = 10,then degrees of freedom for the t statistic is 22.

The F distribution is skewed to the left.

Suppose we are comparing the population variances of two normally distributed populations using independent random samples.If s12=s22s _ { 1 } ^ { 2 } = s _ { 2 } ^ { 2 }s12​=s22​ ,the calculated value of the F statistic will always be equal to one.

In testing the difference between population variances of two normally distributed populations using independent random samples,it is a common practice to compute the F statistic to assess if the value is greater than or equal to one.

Suppose we are testing a null hypothesis about the population mean of a normally distributed population.If the population standard deviation is unknown and n = 14,the appropriate test statistic is based on the ___________ distribution.

In testing the difference between population variances of two normally distributed populations using independent random samples,the F statistic can assume either a positive or a negative value.

A paired difference experiment is an experiment in which there is relationship between the measurements in the different samples.

In a paired difference experiment,a sample of 12 pairs of observations is collected.The degree of freedom for the t statistic is 10.

The F distribution is a symmetric distribution.

When we are comparing the population means from two normally distributed populations based on independent random samples,the pooled estimate of the variance sp2s _ { p } ^ { 2 }sp2​ is used if both population standard deviations are known.

The F distribution is skewed to the right.

In testing the equality of population variances,two assumptions are required: independent samples and normally distributed populations.

Suppose we are comparing two population means from normally distributed populations based on independent random samples and unknown,but equal,population variances.If n₁ = 13 and n₂ = 10,then degrees of freedom for the t statistic is 22.

Suppose we are comparing the population variances of two normally distributed populations using independent random samples.If $s _ { 1 } ^ { 2 } = s _ { 2 } ^ { 2 }$ ,the calculated value of the F statistic will always be equal to one.

When we are comparing the population means from two normally distributed populations based on independent random samples,the pooled estimate of the variance $s _ { p } ^ { 2 }$ is used if both population standard deviations are known.