Question 1

TABLE 9-1
Microsoft Excel was used on a set of data involving the number of defective items found in a random sample of 46 cases of light bulbs produced during a morning shift at a plant. A manager wants to know if the mean number of defective bulbs per case is over 20 during the morning shift. She will make her decision using a test with a level of significance of 0.10. The following information was extracted from the Microsoft Excel output for the sample of 46 cases:
n = 46; Arithmetic Mean = 28.00; Standard Deviation = 25.92; Standard Error = 3.82;
Null Hypothesis: HS1U1B10S1U1B0 : μ ≤ 20.000; α = 0.10; df = 45; T Test Statistic = 2.09;
One-Tail Test Upper Critical Value = 1.3006; p-value = 0.021; Decision = Reject.
-Referring to Table 9-1, the lowest level of significance at which the null hypothesis can be rejected is ________.

Accepted Answer

The answer of TABLE 9-1
Microsoft Excel was used on a...

Question 2

"Is the intended sample size large enough to achieve the desired power of the test for the level of significance chosen?" should be among the questions asked when performing a hypothesis test.

Accepted Answer

This question is relevant to determining the statistical significance and reliability of the test results. A large enough sample size is important to ensure that any observed effects or differences are truly representative of the population, and not simply due to chance. Additionally, having enough power allows for more accurate and confident conclusions to be drawn from the test results.

Question 3

"What conclusions and interpretations can you reach from the results of the hypothesis test?" is not an important question to ask when performing a hypothesis test.

Accepted Answer

This question is very important to ask when performing a hypothesis test because the purpose of the hypothesis test is to determine whether the results support or reject the hypothesis, and to draw conclusions and interpretations from those results.

Question 4

Suppose, in testing a hypothesis about a proportion, the p-value is computed to be 0.034. The null hypothesis should be rejected if the chosen level of significance is 0.01.

Accepted Answer

The answer of Suppose, in testing a hypothesis about a...

Question 5

In a hypothesis test, it is irrelevant whether the test is a one-tail or two-tail test.

Accepted Answer

It is important to determine whether a hypothesis test is one-tailed or two-tailed because it affects the calculation of the p-value and the interpretation of the results. In a one-tailed test, the critical value is located at only one end of the distribution, while in a two-tailed test, the critical values are located at both ends. The determination of which type of test to use should be based on the research question and the direction of the null hypothesis.

Question 6

The statement of the null hypothesis always contains an equality.

Accepted Answer

This is because the null hypothesis assumes that there is no difference or no relationship between the variables being tested, so it usually contains an equality to represent this. For example, "There is no difference in mean scores between Group A and Group B."

Question 7

Suppose, in testing a hypothesis about a proportion, the p-value is computed to be 0.043. The null hypothesis should be rejected if the chosen level of significance is 0.05.

Accepted Answer

Since the p-value (0.043) is less than the chosen level of significance (0.05), the null hypothesis should be rejected.

Question 8

TABLE 9-1
Microsoft Excel was used on a set of data involving the number of defective items found in a random sample of 46 cases of light bulbs produced during a morning shift at a plant. A manager wants to know if the mean number of defective bulbs per case is over 20 during the morning shift. She will make her decision using a test with a level of significance of 0.10. The following information was extracted from the Microsoft Excel output for the sample of 46 cases:
n = 46; Arithmetic Mean = 28.00; Standard Deviation = 25.92; Standard Error = 3.82;
Null Hypothesis: HS1U1B10S1U1B0 : μ ≤ 20.000; α = 0.10; df = 45; T Test Statistic = 2.09;
One-Tail Test Upper Critical Value = 1.3006; p-value = 0.021; Decision = Reject.
-Referring to Table 9-1, the evidence proves beyond a doubt that the mean number of defective bulbs per case is over 20 during the morning shift.

Accepted Answer

The evidence does not prove beyond a doubt; it only shows statistical significance at the 0.10 level, not absolute certainty.

Question 9

In instances in which there is insufficient evidence to reject the null hypothesis, you must make it clear that this has proven that the null hypothesis is true.

Accepted Answer

Insufficient evidence to reject the null hypothesis does not prove that the null hypothesis is true, it simply means there is not enough evidence to reject it.

Question 10

A proper methodology in performing hypothesis tests is to ask whether a random sample can be selected from the population of interest.

Accepted Answer

This is true. Hypothesis testing involves selecting a random sample from a population and assessing whether the results of the sample suggest a significant difference or relationship compared to what would be expected by chance or random variation.

Question 11

In instances in which there is insufficient evidence to reject the null hypothesis, you must make it clear that this does not prove that the null hypothesis is true.

Accepted Answer

Insufficient evidence to reject the null hypothesis only means that there is not enough evidence to support the alternative hypothesis, but it does not necessarily mean that the null hypothesis is true.

Question 12

In testing a hypothesis, you should always raise the question on the purpose of the study, survey or experiment.

Accepted Answer

It is important to always question the purpose of the study, survey or experiment when testing a hypothesis to ensure that the data collected is relevant and meaningful in supporting or rejecting the hypothesis.

Question 13

TABLE 9-1
Microsoft Excel was used on a set of data involving the number of defective items found in a random sample of 46 cases of light bulbs produced during a morning shift at a plant. A manager wants to know if the mean number of defective bulbs per case is over 20 during the morning shift. She will make her decision using a test with a level of significance of 0.10. The following information was extracted from the Microsoft Excel output for the sample of 46 cases:
n = 46; Arithmetic Mean = 28.00; Standard Deviation = 25.92; Standard Error = 3.82;
Null Hypothesis: HS1U1B10S1U1B0 : μ ≤ 20.000; α = 0.10; df = 45; T Test Statistic = 2.09;
One-Tail Test Upper Critical Value = 1.3006; p-value = 0.021; Decision = Reject.
-Referring to Table 9-1, if these data were used to perform a two-tail test, the p-value would be 0.042.

Accepted Answer

The answer of TABLE 9-1
Microsoft Excel was used on a...

Question 14

The test statistic measures how close the computed sample statistic has come to the hypothesized population parameter.

Accepted Answer

This is a true statement. The test statistic is a measure of how many standard errors the sample statistic is away from the hypothesized population parameter under the null hypothesis. It is used to assess the level of evidence that the sample provides against the null hypothesis.

Question 15

Suppose, in testing a hypothesis about a proportion, the Z test statistic is computed to be 2.04. The null hypothesis should be rejected if the chosen level of significance is 0.01 and a two-tail test is used.

Accepted Answer

The critical Z value for a two-tailed test at a 0.01 significance level is approximately ±2.576. Since 2.04 is less than 2.576, the null hypothesis should not be rejected.

Question 16

TABLE 9-1
Microsoft Excel was used on a set of data involving the number of defective items found in a random sample of 46 cases of light bulbs produced during a morning shift at a plant. A manager wants to know if the mean number of defective bulbs per case is over 20 during the morning shift. She will make her decision using a test with a level of significance of 0.10. The following information was extracted from the Microsoft Excel output for the sample of 46 cases:
n = 46; Arithmetic Mean = 28.00; Standard Deviation = 25.92; Standard Error = 3.82;
Null Hypothesis: HS1U1B10S1U1B0 : μ ≤ 20.000; α = 0.10; df = 45; T Test Statistic = 2.09;
One-Tail Test Upper Critical Value = 1.3006; p-value = 0.021; Decision = Reject.
-Referring to Table 9-1, the manager can conclude that there is sufficient evidence to show that the mean number of defective bulbs per case is over 20 during the morning shift using a level of significance of 0.10.

Accepted Answer

The p-value (0.021) is less than the level of significance (0.10), and the decision is to reject the null hypothesis. This means that there is sufficient evidence to support the claim that the mean number of defective bulbs per case is greater than 20 during the morning shift.

Question 17

In conducting research, you should document both good and bad results.

Accepted Answer

Documenting both good and bad results is important in scientific research as it helps in ensuring the reproducibility and reliability of the results. It also helps in identifying any potential biases or errors in the research methodology.

Question 18

TABLE 9-1
Microsoft Excel was used on a set of data involving the number of defective items found in a random sample of 46 cases of light bulbs produced during a morning shift at a plant. A manager wants to know if the mean number of defective bulbs per case is over 20 during the morning shift. She will make her decision using a test with a level of significance of 0.10. The following information was extracted from the Microsoft Excel output for the sample of 46 cases:
n = 46; Arithmetic Mean = 28.00; Standard Deviation = 25.92; Standard Error = 3.82;
Null Hypothesis: HS1U1B10S1U1B0 : μ ≤ 20.000; α = 0.10; df = 45; T Test Statistic = 2.09;
One-Tail Test Upper Critical Value = 1.3006; p-value = 0.021; Decision = Reject.
-Referring to Table 9-1, the manager can conclude that there is sufficient evidence to show that the mean number of defective bulbs per case is over 20 during the morning shift with no more than a 5% probability of incorrectly rejecting the true null hypothesis.

Accepted Answer

The table provides information on the one-tail critical values and p-values for different levels of significance and degrees of freedom in a t-test. Based on the information provided in the output from Excel, the manager can reject the null hypothesis at the 0.10 level of significance and conclude that there is sufficient evidence to support the alternative hypothesis, which states that the mean number of defective bulbs per case is greater than 20. The p-value of 0.021 indicates that the probability of obtaining a sample mean of 28 or higher if the true population mean is 20 or lower is less than 0.021, which is lower than the significance level of 0.10. Therefore, the manager can confidently conclude that the mean number of defective bulbs per case is over 20 during the morning shift with no more than a 5% (or 10%) probability of incorrectly rejecting the true null hypothesis.

Question 19

You should report only the results of hypothesis tests that show statistical significance and omit those for which there is insufficient evidence in the findings.

Accepted Answer

It is important to report all results of hypothesis tests, regardless of whether they show statistical significance or not. Reporting only significant results can lead to publication bias and misinterpretation of the overall findings. It is important to include all results, both significant and non-significant, to provide a complete and accurate representation of the research conducted.

Question 20

TABLE 9-1
Microsoft Excel was used on a set of data involving the number of defective items found in a random sample of 46 cases of light bulbs produced during a morning shift at a plant. A manager wants to know if the mean number of defective bulbs per case is over 20 during the morning shift. She will make her decision using a test with a level of significance of 0.10. The following information was extracted from the Microsoft Excel output for the sample of 46 cases:
n = 46; Arithmetic Mean = 28.00; Standard Deviation = 25.92; Standard Error = 3.82;
Null Hypothesis: HS1U1B10S1U1B0 : μ ≤ 20.000; α = 0.10; df = 45; T Test Statistic = 2.09;
One-Tail Test Upper Critical Value = 1.3006; p-value = 0.021; Decision = Reject.
-Referring to Table 9-1, the manager can conclude that there is sufficient evidence to show that the mean number of defective bulbs per case is over 20 during the morning shift with no more than a 1% probability of incorrectly rejecting the true null hypothesis.

Accepted Answer

The p-value is 0.021, which indicates a 2.1% probability of incorrectly rejecting the null hypothesis, not 1%.

Quiz 9: Fundamentals of Hypothesis Testing: One-Sample Tests