Question 1

The academic planner of a university thinks that at least 35% of the entire student body attends summer school. The correct set of hypotheses to test his belief is

Accepted Answer

The answer of The academic planner of a university thinks...

Question 2

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

Accepted Answer

The student wants to test if the average grade (μ) is at least 85, which translates to a one-tailed test with the alternative hypothesis being that the mean is less than 85 (μ < 85). The null hypothesis, in turn, is that the mean is greater than or equal to 85 (H0: μ ≥ 85). Therefore, the correct set of hypotheses is C) H0: μ ≥ 85 Ha: μ < 85.

Question 3

In hypotheses testing,

Accepted Answer

The answer of In hypotheses testing,
...

Question 4

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

Accepted Answer

The answer of In a two-tailed hypothesis test the test...

Question 5

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

Accepted Answer

At a 95% confidence level, the critical value for a two-tailed test is +/-1.96. If the p-value is greater than 0.05 (the significance level), we fail to reject the null hypothesis. Since the p-value is 0.09, which is greater than 0.05, we cannot reject the null hypothesis. Therefore, the correct choice is B.

Question 6

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

Accepted Answer

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

Question 7

The average life expectancy of tires produced by the Whitney Tire Company has been 40,000 miles. Management believes that due to a new production process, the life expectancy of their tires has increased. In order to test the validity of their belief, the correct set of hypotheses is

Accepted Answer

The null hypothesis should state that the average life expectancy of tires produced by the Whitney Tire Company is equal to or less than 40,000 miles (H0: μ ≤ 40,000), while the alternative hypothesis should state that the average life expectancy is greater than 40,000 miles (Ha: μ > 40,000). This aligns with the management's belief that the new production process has increased the tire's life expectancy.

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

Accepted Answer

The hypothesis test is trying to determine if the recession has led to a reduction in the average work week, so the null hypothesis (H0) should always assume that the population mean (μ) is still 40.1 hours or greater. The alternative hypothesis (Ha) should assume that the mean is less than 40.1 hours if we believe the recession did cause a reduction. Therefore, the best choice is B: H0: μ ≥ 40.1 and Ha: μ < 40.1.

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

Accepted Answer

To test whether there has been a significant increase in the average wage of computer programmers, we need to check if the population mean (μ) is greater than the current average wage of $21.80. Hence, the null hypothesis (H0) should be that the population mean is less than or equal to $21.80 (μ ≤ 21.80) and the alternative hypothesis (Ha) should be that the population mean is greater than $21.80 (μ > 21.80). Therefore, the correct set of hypotheses is H0: μ ≤ 21.80 and Ha: μ > 21.80, which corresponds to option D.

Question 10

In the past, 75% of the tourists who visited Chattanooga went to see Rock City. The management of Rock City recently undertook an extensive promotional campaign. They are interested in determining whether the promotional campaign actually increased the proportion of tourists visiting Rock City. The correct set of hypotheses is

Accepted Answer

The null hypothesis (H0) is that the proportion of tourists visiting Rock City is equal to or less than the previous proportion of 75%. The alternative hypothesis (Ha) is that the proportion of tourists visiting Rock City has increased, so it is greater than 75%. Therefore, the correct set of hypotheses is H0: P ≤ 0.75 Ha: P > 0.75. The other options either have the wrong direction for the alternative hypothesis or the wrong equality sign for the null hypothesis.

Question 11

A soft drink filling machine, when in perfect adjustment, fills the bottles with 12 ounces of soft drink. Any over filling or under filling results in the shutdown and readjustment of the machine. To determine whether or not the machine is properly adjusted, the correct set of hypotheses is

Accepted Answer

The null hypothesis (H0) should reflect the assumption that the machine is properly adjusted, so it should state that the mean amount of soft drink filled is equal to 12 ounces. The alternative hypothesis (Ha) should reflect any deviation from this assumption, so it should state that the mean amount of soft drink filled is not equal to 12 ounces. Therefore, the correct set of hypotheses is H0: μ = 12 and Ha: μ ≠ 12, which is represented by choice D.

Question 12

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

Accepted Answer

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

Question 13

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

Accepted Answer

Since it is a one-tailed lower tail test, we need to find the critical value for a left-tailed t-distribution. With a sample size of 10 and a 90% confidence level, the critical value for a one-tailed lower tail test is -1.383. Therefore, the answer is C.

Question 14

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

Accepted Answer

At 98.4% confidence level for a two-tailed test, the alpha level is 0.016. Using a Z-table, the critical values for a two-tailed test at 0.008 (0.016/2) are approximately ±2.41. Therefore, the correct answer is C.

Question 15

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

Accepted Answer

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

Question 16

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

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 17

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

Accepted Answer

Since this is a one-tailed hypothesis test with a lower tail, we look up the p-value corresponding to the test statistic of -2 in the standard normal distribution table. The p-value is the area to the left of the test statistic, which is 0.0228. Therefore, the best choice is B.

Question 18

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

Accepted Answer

The null hypothesis (H0) should reflect the status quo or no change, which is that the average rent is at least $700. The alternative hypothesis (Ha) should reflect the belief or claim being tested, which is that the average rent has decreased to less than $700.

Question 19

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

Accepted Answer

The correct hypotheses for this scenario would be H0: μ = 5.8 and Ha: μ ≠ 5.8. We want to test if the mean amount of toothpaste being filled in the tubes is equal to 5.8 ounces or not. Therefore, option B is the correct choice.

Question 20

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

Accepted Answer

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

Quiz 9: Hypothesis Tests