Question 1

Read the Z statistic from the normal distribution table and circle the correct answer. A one-tailed test (upper tail) at 87.7% confidence; Z =
A)1.54
B)1.96
C)1.645
D)1.16

Accepted Answer

For an upper tail test at 87.7% confidence, you need to find the Z value corresponding to 1 - 0.877 = 0.123 in the standard normal distribution table, which is approximately 1.16.

Question 2

A machine is designed to fill toothpaste tubes with 5.8 ounces of toothpaste. The manufacturer does not want any underfilling or overfilling. The correct hypotheses to be tested are 
A) 
B) 
C) 
D)

Accepted Answer

The correct hypotheses to be tested are whether the mean amount of toothpaste filled by the machine is equal to 5.8 ounces or not. Therefore, the null hypothesis is that μ = 5.8 and the alternative hypothesis is that μ ≠ 5.8. Option B represents these hypotheses in the correct format. Option A incorrectly labels the null hypothesis as the alternative hypothesis. Option C incorrectly labels the alternative hypothesis as μ > 5.8, which represents overfilling. Option D incorrectly labels the null hypothesis as μ > 5.8, which represents overfilling.

Question 3

A two-tailed test is performed at 95% confidence. The p-value is determined to be 0.09. The null hypothesis
A)must be rejected
B)should not be rejected
C)could be rejected, depending on the sample size
D)has been designed incorrectly

Accepted Answer

Since the p-value is greater than the significance level of 0.05 (corresponding to 95% confidence), the null hypothesis should not be rejected.

Question 4

In a one-tailed hypothesis test (lower tail) the test statistic is determined to be -2. The p-value for this test is
A)0.4772
B)0.0228
C)0.0056
D)0.5228

Accepted Answer

A negative test statistic in a lower-tailed hypothesis test means that the observed sample mean is farther away from the null hypothesis (in the negative direction) than expected by chance. Using a standard normal distribution table, we find that the area to the left of -2 is 0.0228. This is the p-value, which represents the probability of obtaining a sample mean as extreme or more extreme than the observed mean, assuming the null hypothesis is true. A p-value less than the significance level (usually set at 0.05) would lead to rejection of the null hypothesis. Since the p-value in this case is less than 0.05, we can reject the null hypothesis in favor of the alternative hypothesis.

Question 5

For a one-tailed test (upper tail), a sample size of 26 at 90% confidence, t =
A)1.316
B)-1.316
C)-1.740
D)1.740

Accepted Answer

The answer of For a one-tailed test (upper tail), a...

Question 6

For a one-tailed test (lower tail), a sample size of 10 at 90% confidence, t =
A)1.383
B)2.821
C)-1.383
D)-2.821

Accepted Answer

For a lower tail one-tailed test with a sample size of 10 and 90% confidence level, we need to find the critical value of t. Using a t-table with 9 degrees of freedom (n-1), we find the critical value to be -1.383. Since we are looking for a lower tail, the negative value is our critical value. Therefore, the answer is C.

Question 7

For a one-tailed test (lower tail) at 93.7% confidence, Z =
A)-1.86
B)-1.53
C)-1.96
D)-1.645

Accepted Answer

For a lower tail one-tailed test, we need to find the Z-score that has 93.7% of the area to its left. From a Z-table, the closest value to this is 1.54, which corresponds to a 93.32% confidence level. However, since we want a slightly higher level of confidence, we need to shift slightly to the left, which gives us a Z-score of -1.53. Therefore, the answer is B.

Question 8

The average manufacturing work week in metropolitan Chattanooga was 40.1 hours last year. It is believed that the recession has led to a reduction in the average work week. To test the validity of this belief, the hypotheses are 
A) 
B) 
C) 
D)

Accepted Answer

We are interested in comparing the average work week in the current period (after the recession) with the average work week in the past period (before the recession). Therefore, we need to use a one-tailed test. The null hypothesis (H0) is that the average work week is still 40.1 hours (or has not decreased), while the alternative hypothesis (Ha) is that the average work week is now less than 40.1 hours. Option B is the only one that specifies a one-tailed test with a less than sign in the alternative hypothesis. The other options specify two-tailed tests or have incorrect signs in the alternative hypothesis.

Question 9

The average hourly wage of computer programmers with 2 years of experience has been $21.80. Because of high demand for computer programmers, it is believed there has been a significant increase in the average wage of computer programmers. To test whether or not there has been an increase, the correct hypotheses to be tested are 
A) 
B) 
C) 
D)

Accepted Answer

The answer of The average hourly wage of computer programmers...

Question 10

The average monthly rent for one-bedroom apartments in Chattanooga has been $700. Because of the downturn in the real estate market, it is believed that there has been a decrease in the average rental. The correct hypotheses to be tested are 
A) 
B) 
C) 
D)

Accepted Answer

The answer of The average monthly rent for one-bedroom apartments...

Question 11

For a two-tailed test at 98.4% confidence, Z =
A)1.96
B)1.14
C)2.41
D)0.8612

Accepted Answer

To find the Z score for a 98.4% confidence interval, we need to find the value of alpha (α), which is equal to 1 - Confidence Level.

So, α = 1 - 0.984 = 0.016

Since it's a two-tailed test, we need to divide alpha by 2 to find the area in each tail.

So, α/2 = 0.016/2 = 0.008

Looking up the Z score for 0.008 in the Z table, we get 2.41.

Therefore, the Z score for a two-tailed test at 98.4% confidence is 2.41, and the best choice is C.

Question 12

A student believes that the average grade on the final examination in statistics is at least 85. She plans on taking a sample to test her belief. The correct set of hypotheses is A)H₀: $\mu$ < 85 H_a: $\mu$ 85 B)H₀: $\mu$ 85 H_a: $\mu$ > 85 C)H₀: $\mu$ 85 H_a: $\mu$ < 85 D)H₀: $\mu$ > 85 H_a: $\mu$ 85

Accepted Answer

The answer of A student believes that the average grade...

Question 13

For a one-tailed test (upper tail), a sample size of 18 at 95% confidence, t =
A)2.12
B)-2.12
C)-1.740
D)1.740

Accepted Answer

For a one-tailed test (upper tail) with a sample size of 18 and 95% confidence, the critical t-value is positive. With 17 degrees of freedom (n-1), the correct t-value is approximately 1.740.

Question 14

For a one-tailed test (lower tail) at 89.8% confidence, Z =
A)-1.27
B)-1.53
C)-1.96
D)-1.64

Accepted Answer

For a one-tailed lower tail test, the critical Z-score at 89.8% confidence level is -1.27, which is the closest to option A.

Question 15

For a two-tailed test at 86.12% confidence, Z =
A)1.96
B)1.48
C)1.09
D)0.86

Accepted Answer

For a two-tailed test at 86.12% confidence, we want to find the critical values that capture 43.06% in each tail. Using a standard normal distribution table, the closest Z-value to capture 43.06% in one tail is 1.48. Therefore, the best choice is B.

Question 16

For a one-tailed test (upper tail) at 93.7% confidence, Z =
A)1.50
B)1.96
C)1.645
D)1.53

Accepted Answer

For a one-tailed test at 93.7% confidence, the critical value corresponds to the 6.3% in the upper tail. The Z-value for this is approximately 1.53.

Question 17

In a two-tailed hypothesis test the test statistic is determined to be Z = -2.5. The p-value for this test is
A)-1.25
B)0.4938
C)0.0062
D)0.0124

Accepted Answer

The p-value for a two-tailed test with Z = -2.5 is 2 times the area to the left of Z = -2.5, which is approximately 0.0062, so the p-value is 0.0124.

Question 18

For a one-tailed test (lower tail) with 22 degrees of freedom at 95% confidence, the value of t =
A)-1.383
B)1.383
C)-1.717
D)-1.721

Accepted Answer

The answer of For a one-tailed test (lower tail) with...

Question 19

For a one-tailed hypothesis test (upper tail) the p-value is computed to be 0.034. If the test is being conducted at 95% confidence, the null hypothesis
A)could be rejected or not rejected depending on the sample size
B)could be rejected or not rejected depending on the value of the mean of the sample
C)is not rejected
D)is rejected

Accepted Answer

Since the p-value is less than our chosen significance level of 0.05 (corresponding to 95% confidence), we reject the null hypothesis.

Question 20

For a two-tailed test, a sample of 20 at 80% confidence, t =
A)1.328
B)2.539
C)1.325
D)2.528

Accepted Answer

The correct answer is A because the t-value for a two-tailed test with a sample size of 20 and a confidence level of 80% is 1.328.

Quiz 9: Hypothesis Tests

Read the Z statistic from the normal distribution table and circle the correct answer. A one-tailed test (upper tail) at 87.7% confidence; Z =

A machine is designed to fill toothpaste tubes with 5.8 ounces of toothpaste. The manufacturer does not want any underfilling or overfilling. The correct hypotheses to be tested are

A two-tailed test is performed at 95% confidence. The p-value is determined to be 0.09. The null hypothesis

In a one-tailed hypothesis test (lower tail) the test statistic is determined to be -2. The p-value for this test is

For a one-tailed test (upper tail) , a sample size of 26 at 90% confidence, t =

For a one-tailed test (lower tail) , a sample size of 10 at 90% confidence, t =

For a one-tailed test (lower tail) at 93.7% confidence, Z =

The average manufacturing work week in metropolitan Chattanooga was 40.1 hours last year. It is believed that the recession has led to a reduction in the average work week. To test the validity of this belief, the hypotheses are

The average monthly rent for one-bedroom apartments in Chattanooga has been $700. Because of the downturn in the real estate market, it is believed that there has been a decrease in the average rental. The correct hypotheses to be tested are

For a two-tailed test at 98.4% confidence, Z =

A student believes that the average grade on the final examination in statistics is at least 85. She plans on taking a sample to test her belief. The correct set of hypotheses is

For a one-tailed test (upper tail) , a sample size of 18 at 95% confidence, t =

For a one-tailed test (lower tail) at 89.8% confidence, Z =

For a two-tailed test at 86.12% confidence, Z =

For a one-tailed test (upper tail) at 93.7% confidence, Z =

In a two-tailed hypothesis test the test statistic is determined to be Z = -2.5. The p-value for this test is

For a one-tailed test (lower tail) with 22 degrees of freedom at 95% confidence, the value of t =

For a one-tailed hypothesis test (upper tail) the p-value is computed to be 0.034. If the test is being conducted at 95% confidence, the null hypothesis

For a two-tailed test, a sample of 20 at 80% confidence, t =