Question 1

A z test of proportions is used when a hypothesis test is conducted on a population proportion.

Accepted Answer

A z test of proportions is specifically designed to test hypotheses about population proportions, comparing the observed proportion to a theoretical expectation under the null hypothesis.

Question 2

When the population standard deviation ($\sigma$ )is unknown, the value of s - 1 is used to compute the t value.

Accepted Answer

When the population standard deviation is unknown, the sample standard deviation (s) is used directly in the formula for the t value; the term "s - 1" refers to the degrees of freedom (n - 1) where n is the sample size, not a modification of the standard deviation.

Question 3

When using the t test to test a hypothesis about a population mean with an unknown population standard deviation ($\sigma$ )the degrees of freedom is defined as n - 1.

Accepted Answer

When using the t-test for a population mean with an unknown population standard deviation, the degrees of freedom (df) is calculated as the sample size (n) minus one (n - 1). This is because one degree of freedom is lost in estimating the population mean from the sample mean.

Question 4

A "scientific hypothesis" _______________.
A)is a synonym for the term "scientific theory."
B)is disproven if a counterexample is found.
C)is a tentative explanation of some natural phenomena.
D)is a proven explanation of some natural phenomena.
E)may or may not be testable.

Accepted Answer

A scientific hypothesis is a tentative explanation of some natural phenomena.

Question 5

Suppose that H_o: $\mu$$\le$ 0.01 H_a: $\mu$> 0.01 The value 0.01 is the maximum safe level of some naturally occurring lethal pollutant in drinking water for human consumption.You need to decide if you will use water coming from a specific source for one of the beverages your company produces, based on sample measures of this pollutant taken in random different locations and times at the source of water.In this case you would want to A)maximize the power of the test. B)maximize β. C)minimize $\mu$. D)maximize the significance, α. E)maximize 1 - α.

Accepted Answer

Maximizing the power of the test ensures that if the pollutant level is indeed above the safe threshold, the test is more likely to correctly reject the null hypothesis (that the water is safe). This minimizes the risk of using unsafe water.

Question 6

A statistically significant result is _______________.
A)a result that is likely due to chance.
B)a result that is unlikely due to chance.
C)the same as a substantive result.
D)a result that is important for decision makers.
E)a result that leads to the rejection of the alternative hypothesis.

Accepted Answer

A statistically significant result indicates that the observed effect is unlikely to have occurred by chance alone, suggesting a real effect or difference exists in the population from which the sample was drawn.

Question 7

The value of committing a Type II error is defined by the researcher prior to the study.

Accepted Answer

A Type II error, or failing to reject a false null hypothesis, is not defined by the researcher but rather is a risk associated with the study's design and statistical power.

Question 8

Increasing the sample size reduces the probability of committing a Type I and Type II simultaneously.

Accepted Answer

Increasing the sample size reduces the probability of committing a Type II error (failing to reject a false null hypothesis), but it does not affect the probability of committing a Type I error (rejecting a true null hypothesis).

Question 9

If the p-value for a one-tailed test is 0.019, then the null hypothesis
A)can be rejected at a significance level of 0.01.
B)would be rejected or not rejected depending on the value of the statistic (the observed value).
C)would be rejected or not rejected depending on the value of the statistic and the critical value.
D)can be rejected at a significance level of 0.10.
E)may or may not be rejected, but there is no enough information to answer this question.

Accepted Answer

The p-value of 0.019 indicates that there is a 1.9% chance of observing the data (or something more extreme) if the null hypothesis were true. Since this p-value is less than 0.10, the null hypothesis can be rejected at a significance level of 0.10, but not at more stringent levels such as 0.01.

Question 10

The probability of committing a Type II error changes for each alternative value of the parameter.

Accepted Answer

The probability of committing a Type II error, denoted by β, varies depending on the specific alternative value of the parameter being tested against the null hypothesis. Different alternative parameter values can have different probabilities of not being detected when the null hypothesis is falsely accepted.

Question 11

In testing a hypothesis about a population mean with an unknown population standard deviation ($\sigma$ )the degrees of freedom is used in the denominator of the test statistic.

Accepted Answer

When testing a hypothesis about a population mean with an unknown population standard deviation, the sample standard deviation is used to estimate the population standard deviation, and the degrees of freedom (df) are used to determine the critical values from the t-distribution, not in the denominator of the test statistic. The test statistic itself is calculated using the sample mean, hypothesized population mean, sample standard deviation, and sample size.

Question 12

If the observed chi-squared value is more than the critical chi-squared value found on the related table, then the null hypothesis is rejected.

Accepted Answer

When the observed chi-squared value exceeds the critical chi-squared value from the table (at a given significance level), it indicates that the observed data significantly deviate from what was expected under the null hypothesis, leading to its rejection.

Question 13

A business is testing a new product that in reality would make the company money.Based on market research data, the business analyst committed a Type II error by rejecting the null.

Accepted Answer

A Type II error occurs when the null hypothesis is not rejected when it is false. If the analyst rejected the null hypothesis, they did not commit a Type II error.

Question 14

If car manufacturer of cars orders the windshields from another company.The width of the windshields received need to be within 0.2 mm of the average width.The contract between the car manufacturer and the windshield suppler should include a clause related to the delivered windshields' median.

Accepted Answer

The contract should focus on the precision around the average (mean) width, not the median, as the requirement is for the windshields to be within 0.2 mm of the average width.

Question 15

Business researchers sometimes need to test for equality of population variance.The hypothesis test about a population variance is performed using a chi-square test.

Accepted Answer

The chi-square test is indeed used by researchers to test for the equality of population variances among groups, which is a common requirement in statistical analysis to ensure the validity of various other tests, such as ANOVA, that assume homogeneity of variances.

Question 16

The p-value is A)the probability that the alternative hypothesis is true. B)the probability that the null hypothesis is true. C)the probability of a statistic being at most as extreme as the observed value when H_o is true. D)the probability of a statistic being at most as extreme as the observed value when H_o is false. E)the probability of a statistic being at least as extreme as the observed value when H_o is true.

Accepted Answer

The p-value is the probability of observing a test statistic at least as extreme as the one observed, assuming that the null hypothesis is true.

Question 17

When conducting a hypothesis test on a population proportion, the value of q is defined as p + 1.

Accepted Answer

In the context of hypothesis testing on a population proportion, $q$ is defined as $1 - p$, where $p$ is the hypothesized population proportion. $q$ represents the proportion of failures or the complement of $p$.

Question 18

In conducting the z test of proportions, the sample proportion is computed by dividing the number of items being counted by the estimated total population.

Accepted Answer

The sample proportion is computed by dividing the number of items being counted by the total number of items in the sample, not the estimated total population.

Question 19

If the null hypothesis is in reality false, but the sample data leads the analyst to fail to reject the null, then the analysts has made a Type II error.

Accepted Answer

A Type II error occurs when the null hypothesis is false, but the data do not provide sufficient evidence to reject it, leading to a false negative conclusion.

Question 20

In testing a hypothesis about a population variance, the chi-square test is fairly robust to the assumption the population is normally distributed.

Accepted Answer

The chi-square test for a population variance is sensitive to the normality assumption, meaning the test's validity depends on the data being normally distributed.

Quiz 9: Statistical Inference: Hypothesis Testing for Single Populations

A z test of proportions is used when a hypothesis test is conducted on a population proportion.

When the population standard deviation ( $\sigma$ )is unknown, the value of s - 1 is used to compute the t value.

When using the t test to test a hypothesis about a population mean with an unknown population standard deviation ( $\sigma$ )the degrees of freedom is defined as n - 1.

A "scientific hypothesis" _______________.

A statistically significant result is _______________.

The value of committing a Type II error is defined by the researcher prior to the study.

Increasing the sample size reduces the probability of committing a Type I and Type II simultaneously.

If the p-value for a one-tailed test is 0.019, then the null hypothesis

The probability of committing a Type II error changes for each alternative value of the parameter.

In testing a hypothesis about a population mean with an unknown population standard deviation ( $\sigma$ )the degrees of freedom is used in the denominator of the test statistic.

If the observed chi-squared value is more than the critical chi-squared value found on the related table, then the null hypothesis is rejected.

A business is testing a new product that in reality would make the company money.Based on market research data, the business analyst committed a Type II error by rejecting the null.

If car manufacturer of cars orders the windshields from another company.The width of the windshields received need to be within 0.2 mm of the average width.The contract between the car manufacturer and the windshield suppler should include a clause related to the delivered windshields' median.

Business researchers sometimes need to test for equality of population variance.The hypothesis test about a population variance is performed using a chi-square test.

The p-value is

When conducting a hypothesis test on a population proportion, the value of q is defined as p + 1.

In conducting the z test of proportions, the sample proportion is computed by dividing the number of items being counted by the estimated total population.

If the null hypothesis is in reality false, but the sample data leads the analyst to fail to reject the null, then the analysts has made a Type II error.

In testing a hypothesis about a population variance, the chi-square test is fairly robust to the assumption the population is normally distributed.

Quiz 9: Statistical Inference: Hypothesis Testing for Single Populations

A z test of proportions is used when a hypothesis test is conducted on a population proportion.

When the population standard deviation ( σ\sigmaσ )is unknown, the value of s - 1 is used to compute the t value.

When using the t test to test a hypothesis about a population mean with an unknown population standard deviation ( σ\sigmaσ )the degrees of freedom is defined as n - 1.

A "scientific hypothesis" _______________.

A statistically significant result is _______________.

The value of committing a Type II error is defined by the researcher prior to the study.

Increasing the sample size reduces the probability of committing a Type I and Type II simultaneously.

If the p-value for a one-tailed test is 0.019, then the null hypothesis

The probability of committing a Type II error changes for each alternative value of the parameter.

In testing a hypothesis about a population mean with an unknown population standard deviation ( σ\sigmaσ )the degrees of freedom is used in the denominator of the test statistic.

If the observed chi-squared value is more than the critical chi-squared value found on the related table, then the null hypothesis is rejected.

A business is testing a new product that in reality would make the company money.Based on market research data, the business analyst committed a Type II error by rejecting the null.

If car manufacturer of cars orders the windshields from another company.The width of the windshields received need to be within 0.2 mm of the average width.The contract between the car manufacturer and the windshield suppler should include a clause related to the delivered windshields' median.

Business researchers sometimes need to test for equality of population variance.The hypothesis test about a population variance is performed using a chi-square test.

The p-value is

When conducting a hypothesis test on a population proportion, the value of q is defined as p + 1.

In conducting the z test of proportions, the sample proportion is computed by dividing the number of items being counted by the estimated total population.

If the null hypothesis is in reality false, but the sample data leads the analyst to fail to reject the null, then the analysts has made a Type II error.

In testing a hypothesis about a population variance, the chi-square test is fairly robust to the assumption the population is normally distributed.

When the population standard deviation ( $\sigma$ )is unknown, the value of s - 1 is used to compute the t value.

When using the t test to test a hypothesis about a population mean with an unknown population standard deviation ( $\sigma$ )the degrees of freedom is defined as n - 1.

In testing a hypothesis about a population mean with an unknown population standard deviation ( $\sigma$ )the degrees of freedom is used in the denominator of the test statistic.