Statistics Midterm

Which of the following would compute a CRITICAL VALUE for a​ 96% level of confidence to estimate the population mean when sigma is known and the sample size is 25. =T.INV(0.02,24) =T.INV.2T(0.04,24) =NORMSINV(0.02) =NORMSINV(0.04)

=NORMSINV(0.02)

Assuming a normal distribution, as the standard deviation increases, the shape of curve: does not change. shifts right. becomes taller and narrower. becomes shorter and wider.

becomes shorter and wider

Food inspectors inspect samples of food products to see if they are safe. This can be thought of as a hypothesis test with the following hypotheses. H0: the food is safe Ha: the food is not safe The following is an example of what type of error? The sample suggests that the food is contaminated, but it actually is safe. type I type II not an error

type I

The null hypothesis for all chi-square tests assumes the observed data (frequencies) in a sample is different from what we expect of a given population. True, the null assumes a difference exists between our observations and expectations. False, the null is status quo and assumes no difference exists between our observations and expectations. LicensePoints possible: 1

False, the null is status quo and assumes no difference exists between our observations and expectations.

A​ p-value is the probability of observing a value of a statistic or a value that is more unusual just by chance. True, the p-value does not depend on the null hypothesis. False, this statement would be true if it included the phrase, assuming the null hypothesis is true.

False, this statement would be true if it included the phrase, assuming the null hypothesis is true.

A medical study was investigating if getting a flu shot actually reduced the risk of developing the flu. A hypothesis test is performed. Which of the following will result in a Type I​ error? Researchers could not tell if the flu shot reduced the risk of developing the flu because of other problems with the study. Researchers said the flu shot reduced the risk of developing the flu when it actually​ didn't. Researchers said the flu shot did not reduce the risk of developing the flu when it actually did. Researchers said the flu shot reduced the risk of developing the flu when it actually did. Researchers said the flu shot did not reduce the risk of developing the flu when it actually​ didn't.

Researchers said the flu shot reduced the risk of developing the flu when it actually​ didn't.

Days before a presidential​ election, an article based on a nationwide random sample of registered voters reported the following​ statistic, "52% ​(plus or minus​3%) of registered voters will vote for Robert​ Smith." What is the ​"plus or minus​ 3%" ​called? sample proportion margin of error standard error confidence interval for a proportion

margin of error

As the standard deviation of a normal curve decreases, the data becomes __________ centered around the mean. less more

more

For a given degrees of freedom, the larger the chi-square statistic, the ________________ evidence there is to reject the null hypothesis. less more same amount of

more

The larger the sample, the __________ accurate the sample mean will be as an estimate of the population mean. less more

more

Failing to reject an invalid null hypothesis (continuing to incorrectly assume a null is valid) is called: the level of confidence. the level of significance. the alpha-risk. the power of the test. the beta-risk.

the beta-risk.

You obtain a sample chi-square test statistic of -5.49. On the basis of this value, you know that there is a negative association between your two variables. the observed frequencies are lower than the expected frequencies across all categories. you have made a calculation error; chi-square values cannot be negative. the observed frequencies are higher than the expected frequencies across at least half of the categories.

you have made a calculation error; chi-square values cannot be negative.

The degrees of freedom for a 3 x 3​ cross-tabulation table for the​ chi-square test of independence equal

4

According to the Empirical​ Rule, 95% of the area under the normal curve is within two standard deviations of the mean. What percent of the area under the normal curve is more than two standard deviations from the​ mean? 5% 2.5% 10%. There is not enough information to determine the percent.

5%

Although​ rare, it is possible to get a​ p-value from a​ two-sided test greater than 1. True False

False

If a z-score is equal to zero, which of the following must be true? The x-value must be equal to the mean of the distribution. The​ x-value must be greater than the mean of the distribution. The x-value must equal zero. The mean must equal zero.

The x-value must be equal to the mean of the distribution

Suppose increasing the sample size will not change the sample mean or the standard deviation. What will happen to the​ p-value by increasing the sample​ size? The​ p-value will increase. The​ p-value will decrease. The​ p-value will not change. More information is needed to determine what will happen to the​ p-value.

The​ p-value will decrease.

All else equal, an increase in sample size will cause a(n) decrease increase in the size of a confidence interval.

Decrease

Benjamin performed a​ two-tailed one-sample​ t-test and obtained a ​p-value equal to 1. What conclusion should he​ make? He did something wrong as it is not possible to get a​ p-value equal to 1. He should accept the null hypothesis as true. His standard error must have been 0. His sample mean must have been exactly equal to his hypothesized value for the population mean. All his observations must have been the same.

His sample mean must have been exactly equal to his hypothesized value for the population mean.

Days before a presidential​ election, a nationwide random sample of registered voters was taken. Based on this random​ sample, it was reported that​ "52% of registered voters plan on voting for Robert Smith with a margin of error of plus or minus​3%." The margin of error was based on a​ 95% confidence level. Can we say with​ 95% confidence that Robert Smith will win the election if he needs a simple majority of votes to​ win? Yes, since over​ 50% of the voters in the sample say they will vote for Robert Smith. No, because​ 50% is within the bounds of the confidence interval. Yes, because​ 50% is within the bounds of the confidence interval. No, because the margin of error can never be more than​ 1%.

No, because​ 50% is within the bounds of the confidence interval.

The​ vice-president of operations wondered if the average strength of wire cables was different between those produced at the​ company's plant in a rural location and those produced in the​ company's plant located in a large city. Which of the following is the correct statement of what a Type II Error is in the context of this​ problem? The VP did not have evidence to say that there was a difference in the average cable strengths between the two locations and there really was no difference in the average strengths. The VP had evidence to say that there was a difference in the average cable strengths between the two locations when in fact there was no difference in the average strengths. The VP did not have evidence to say that there was a difference in the average cable strengths between the two locations when in fact there was a difference in the average strengths. The VP had evidence to say that there was a difference in the average cable strengths between the two locations and there really was a difference in the average strengths.

The VP did not have evidence to say that there was a difference in the average cable strengths between the two locations when in fact there was a difference in the average strengths.

When will a chi-square statistic be 0? When all expected counts are 0. When the number of cells with expected counts greater than their observed counts is the same as the number of cells with expected counts less than their observed counts. When all observed counts are the same as their expected counts. When the difference between the expected counts and observed counts average to 0.

When all observed counts are the same as their expected counts.

The claim that is assumed to be true in a hypothesis test is called: the power. the p-value. the null hypothesis. the alternative hypothesis.

the null hypothesis.

Which of the following represents the probability of correctly rejecting an invalid null hypothesis? the beta-risk. the alpha-risk. the level of significance. the power of the test. the level of confidence.

the power of the test.

Researchers can make the results statistically significant by increasing the sample size even if the difference between the sample mean and hypothesized value of the population mean is very small. true false

true

In a Chi-Square test, which of the following is NOT​ true? The null hypothesis is that the different populations have the same proportions of specified characteristics. Small values of the chi squared test statistic would lead to a decision to reject the null hypothesis. If the chi squared test statistic is​ large, the​ P-value will be small. Samples are drawn from different populations and we wish to determine whether these populations have the same proportions of the characteristics being considered.

Small values of the chi squared test statistic would lead to a decision to reject the null hypothesis.

Which of the following formulas would you use to compute a critical value for a 92% level of confidence to estimate the population mean given a sample standard deviation of 10 and a sample size of 35, =T.INV.2T(0.92,34) =NORMSINV(0.96) =NORMSINV(0.92) =NORMSINV(0.08) =T.INV(0.96,35) =T.INV.2T(0.08,34)

T.INV.2T(0.08,34)

The purpose of a Chi-Square test is to examine the relationship between an explanatory categorical variable and a response quantitative variable examine the relationship between an explanatory quantitative variable and a response categorical variable examine relationships between two quantitative variables. examine relationships between two categorical variables. None of the above are true

examine relationships between two categorical variables.

The possible values that we believe a population mean will be with a certain level of confidence is the margin of error. always contains the true parameter. form a confidence interval for the population mean. form the sampling distribution.

form a confidence interval for the population mean

When sampling and the standard deviation is not known, what is used to estimate it? the standard deviation of the distribution of sample means the​ t-distribution the standard error of the distribution of sample means the standard deviation of the data from the sample

the standard deviation of the data from the sample

Which of the following would compute a CRITICAL VALUE for a​ 96% level of confidence to estimate the population mean when sigma is known and the sample size is 25. =T.INV.2T(0.04,25) =T.INV(0.04,24) =T.INV(0.02,25) =NORMSINV(0.04) =T.INV.2T(0.04,24) =NORMSINV(0.96) =NORMSINV(0.02) LicensePoints possible: 1Unlimited attempts.

=NORMSINV(0.02)

Which of the following formulas would you use to compute a critical value for a 95% level of confidence to estimate the population mean given an assumed standard deviation of 10 and a sample size of 35, =T.INV.2T(0.95,34) =NORMSINV(0.025) =NORMSINV(0.95) =T.INV.2T(0.05,34) =T.INV(0.975,35) =NORMSINV(0.05)

=NORMSINV(0.025)

The p-value for a hypothesis test turns out to be 0.09627. At a 5% level of significance, what is the proper decision? Reject H0H0 Fail to reject H0

Fail to reject H0

You are performing a two-tailed z-testIf α=0.01α=0.01, and your test statistic is z=1.84z=1.84, do you: Fail to Reject Null Hypothesis Reject Null Hypothesis

Fail to Reject Null Hypothesis

Which of the following is a correct explanation of what a confidence interval​ is? A confidence interval gives a range of possible values for the mean of those in the sample with a certain level of confidence. The confidence level is the probability the interval actually contains the population​ parameter, assuming that the estimation process is repeated a large number of times. A confidence interval is a range of values used to estimate the true value of a population parameter. A confidence interval gives two values​ (called the lower bound and upper​ bound) that the population mean could be with a certain level of confidence. A confidence interval indicates how far off​ we're willing to be from the population mean with a certain level of confidence. A confidence interval gives an exact value for the population mean with a certain level of confidence.

A confidence interval is a range of values used to estimate the true value of a population parameter

A critical value is _____________. A critical value is how far away our sample statistic can be from the true population parameter with a certain level of confidence. A critical value is the value that best estimates a population parameter. A critical value is the number of standard errors​ (or standard​ deviations) to move from the mean of a sampling distribution to correspond to a specified level of confidence. A critical value is the probability of obtaining a sample statistic like the one obtained from the sample or something more unusual if the null hypothesis is true.

A critical value is the number of standard errors​ (or standard​ deviations) to move from the mean of a sampling distribution to correspond to a specified level of confidence.

A medical study was investigating whether getting a flu shot actually reduced the risk of developing the flu. A hypothesis test is to be performed. Which of the following statements is​ correct? A​ two-tailed test will be performed since the null hypothesis states that the parameter is not equal to the hypothesized valued. A​ one-tailed test will be performed since the alternative hypothesis states that the parameter is less than the hypothesized value. A​ one-tailed test will be performed since the alternative hypothesis states that the parameter is not equal to the hypothesized value. A​ two-tailed test will be performed since the alternative hypothesis states that the parameter is not equal to the hypothesized value. A​ two-tailed test will be performed since the alternative hypothesis states that the parameter is less than they hypothesized value.

A​ one-tailed test will be performed since the alternative hypothesis states that the parameter is less than the hypothesized value.

The​ vice-president of operations wondered if the average strength of wire cables was different between those produced at the​ company's plant in a rural location and those produced in the​ company's plant located in a large city. Which of the following statements is​ correct? A​ two-tail test will be performed since the null hypothesis contains a​ not equal​ to. A​ two-tail test will be performed since the alternative hypothesis contains a​ not equal​ to. A​ two-tail test will be performed since the alternative hypothesis contains a​ less than. A​ one-tail test will be performed since the alternative hypothesis contains either a​ greater than or a​ less than. A​ one-tail test will be performed since the alternative hypothesis contains a​ not equal​ to.

A​ two-tail test will be performed since the alternative hypothesis contains a​ not equal​ to.

Researchers conducted a study and obtained a p-value of 0.85. Because the p-value is quite high, there is evidence to accept the null hypothesis. False. We do not accept a null hypothesis. The large p-value indicates that there is a high probability that we would have gathered our evidence assuming the null is valid. Thus, there is not enough evidence to reject the null hypothesis and so we continue to assume it is valid. True. The large p-value indicates a high probability that the null is valid. Thus, there is enough evidence to accept the null hypothesi

False. We do not accept a null hypothesis. The large p-value indicates that there is a high probability that we would have gathered our evidence assuming the null is valid. Thus, there is not enough evidence to reject the null hypothesis and so we continue to assume it is valid.

A student wondered if more than 10% of students enrolled in an introductory Chemistry class dropped before the midterm. Suppose he performed a hypothesis test to test his claim. In the context of the problem, what would happen if the student made a Type II Error? He claims that 10% of students in the introductory Chemistry class dropped before the midterm when, in fact, more than 10% actually dropped. He claims that 10% (or less) of students in the introductory Chemistry class dropped before the midterm when, in fact, more than 10% really did drop the class. He claims that more than 10% of students in the introductory Chemistry class dropped before the midterm when, in fact, more than 10% really did drop the class. He claims that 10% (or less) of students in the introductory Chemistry class dropped before the midterm when, in fact, 10% (or less) actually dropped.

He claims that 10% (or less) of students in the introductory Chemistry class dropped before the midterm when, in fact, more than 10% really did drop the class.

A student wondered if more than 10% of students enrolled in an introductory Chemistry class dropped before the midterm. Suppose he performed a hypothesis test to test his claim. In the context of the problem, what would happen if the student made a Type I Error? He claims that more than 10% of students in the introductory Chemistry class dropped before the midterm when, in fact, 10% (or less) actually dropped. He claims that 10% of students in the introductory Chemistry class dropped before the midterm when, in fact, more than 10% actually dropped. He claims that 10% of students in the introductory Chemistry class dropped before the midterm when, in fact, 10% really did drop the class. He claims that more than 10% of students in the introductory Chemistry class dropped before the midterm when, in fact, more than 10% really did drop the class.

He claims that more than 10% of students in the introductory Chemistry class dropped before the midterm when, in fact, 10% (or less) actually dropped.

At a stop sign, some drivers come to a full stop, some come to a `rolling stop' (not a full stop, but slow down), and some do not stop at all. We would like to test if there is an association between gender and type of stop (full, rolling, or no stop). We collect data by standing a few feet from a stop sign and taking note of type of stop and the gender of the driver. What are the hypotheses for testing for an association between gender and type of stop? Ho: Gender and type of stop are independent. Ha: Gender and type of stop are not independent. Ho: Males and females are equally likely to come to a full stop. Ha: Males and females are not equally likely to come to a full stop. Ho: Males and females are equally likely to come to a rolling stop. Ha: Males are more likely than females to come to a rolling stop. Ho: Gender and type of stop are not independent. Ha: Gender and type of stop are independent.

Ho: Gender and type of stop are independent. Ha: Gender and type of stop are not independent.

All else equal, an increase in the level of confidence will cause a(n) decrease increase in the size of a confidence interval.

Increase

Which of the following would increase the width of a confidence interval for a population mean? Increase the level of confidence Increase the sample size Decrease the sample standard deviation All of the above

Increase the level of confidence

Which of the following facts about the p-value of a test is correct? The p-value is calculated under the assumption that the null hypothesis is true. The smaller the p-value, the more evidence the data provide against H0. The p-value can have values between -1 and 1. All of the above are correct. Just (A) and (B) are correct.

Just (A) and (B) are correct.

Which is greater in a normal​ distribution, the mean or the​ median? Explain. Neither; the mean and median are always equal in a normal​ distribution, since it is symmetric. Median; the median is always greater than the median in a normal distribution. It depends on the particular normal distribution. Mean; the mean is always greater than the median in a normal distribution.

Neither; the mean and median are always equal in a normal​ distribution, since it is symmetric.

Days before a presidential​ election, a nationwide random sample of registered voters was taken. Based on this random​ sample, it was reported that​ "52% of registered voters plan on voting for Robert Smith with a margin of error of plus or minus​3%." The margin of error was based on a​ 95% confidence level. Can we say with​ 95% confidence that Robert Smith will win the election if he needs a simple majority of votes to​ win? No, because​ 50% is within the bounds of the confidence interval. Yes, because​ 50% is within the bounds of the confidence interval. No, because the margin of error can never be more than​ 1%. Yes, since over​ 50% of the voters in the sample say they will vote for Robert Smith.

No, because​ 50% is within the bounds of the confidence interval.

Can a critical value for the chi squared​-test be​ negative? Explain. Yes, in a chi squared​-distribution, half of the chi squared​-values are less than​ 0, and half of the chi squared​-values are greater than 0. Yes, in a chi squared​-distribution, all chi squared​-values are less than 0. No, in a chi squared​-distribution, all chi squared​-values are greater than or equal to 100. No, in a chi squared​-distribution, all chi squared​-values are greater than or equal to 0.

No, in a chi squared​-distribution, all chi squared​-values are greater than or equal to 0.

Which of the following is NOT true for conducting a hypothesis test for independence between the row variable and column variable in a contingency​ table? Small values of the chi squared test statistic reflect significant differences between observed and expected frequencies. The number of degrees of freedom is (r-1)(c-1), where r is the number of rows and c is the number of columns. The null hypothesis is that the row and column variables are independent of each other. Tests of independence with a contingency table are always​ right-tailed.

Small values of the chi squared test statistic reflect significant differences between observed and expected frequencies.

Why does sample size need to be accounted for in the t-distribution? The t-distribution should not be used for large sample sizes. The t-distribution changes for different sample sizes. The accuracy of the t-distribution depends on the sample size. The t-distribution should not be used for small sample sizes. The t-distribution becomes less skewed as the sample size increases.

The t-distribution changes for different sample sizes.

A commonly cited standard for one-way length (duration) of school bus rides for elementary school children is 30 minutes. A local government office in a rural area conducts a study to determine if elementary schoolers in their district have a longer average one-way commute time. If they determine that the average commute time of students in their district is significantly higher than the commonly cited standard they will invest in increasing the number of school busses to help shorten commute time. What would a Type II error mean in this context? The local government decides that the data provide convincing evidence of an average commute time higher than 30 minutes, when the true average commute time is in fact 30 minutes. The local government decides that the average commute time is 30 minutes. The local government decides that the data do not provide convincing evidence of an average commute time higher than 30 minutes, when the true average commute time is in fact higher than 30 minutes. The local government decides that the data do not provide convincing evidence of an average commute time different than 30 minutes, when the true average commute time is in fact 30 minutes.

The local government decides that the data do not provide convincing evidence of an average commute time higher than 30 minutes, when the true average commute time is in fact higher than 30 minutes.

A commonly cited standard for one-way length (duration) of school bus rides for elementary school children is 30 minutes. A local government office in a rural area conducts a study to determine if elementary schoolers in their district have a longer average one-way commute time. If they determine that the average commute time of students in their district is significantly higher than the commonly cited standard they will invest in increasing the number of school busses to help shorten commute time. What would a Type I error mean in this context? The local government decides that the data do not provide convincing evidence of an average commute time different than 30 minutes, when the true average commute time is in fact 30 minutes. The local government decides that the data do not provide convincing evidence of an average commute time higher than 30 minutes, when the true average commute time is in fact higher than 30 minutes. The local government decides that the data provide convincing evidence of an average commute time higher than 30 minutes, when the true average commute time is in fact 30 minutes. The local government decides that the average commute time is 30 minutes.

The local government decides that the data provide convincing evidence of an average commute time higher than 30 minutes, when the true average commute time is in fact 30 minutes.

Abbie performs a​ hypothesis test and obtains a​ t-statistic of 0. Based on this​ information, which of the following is NOT true. The sample mean is the same as the hypothesized value of the population mean The standard error is 0 If Abbie performed another sample with a larger sample size and obtained the same sample​ mean, the​ p-value would remain the same. the one-sided p-value is 0.5 The​ two-sided p-value is 1

The standard error is 0

Health-care workers who use latex gloves with glove powder on a daily basis are particularly susceptible to developing a latex allergy. Each worker in a sample of 30 hospital employees who were diagnosed with a latex allergy was asked how many latex gloves they used per week. A​ 99% confidence interval was​ (17 gloves/week, 25​ gloves/week). What would happen if a sample of 40 employees was taken​ instead? The width of the confidence interval would decrease. The width of the confidence interval would increase. The width of the confidence interval would stay the same. More information is needed to know how the width of the confidence interval would​ change, if at all.

The width of the confidence interval would decrease

What would happen to the width of a confidence interval if the level of confidence increased (assuming everything else remained the same)? The width of the confidence interval would stay the same. More information is needed to determine how the width would change. The width of the confidence interval would increase. The width of the confidence interval would decrease.

The width of the confidence interval would increase.

A study was conducted based on a sample size of 30 individuals. The​ p-value was 0.10. Suppose a researcher conducted another study by taking a random sample of 50 individuals from the same population. Suppose they obtained the same sample mean as in the first study with a sample size of 30.​ (Also assume the population standard deviation is the same for both​ studies.) Which of the following is​ true? The​ p-value would be larger for the second study. The​ p-value would be the same for both studies. The​ p-value would be smaller for the second study. More information is needed to compare the​ p-values from both studies.

The​ p-value would be smaller for the second study.

A​ p-value is the probability that the null hypothesis is true. This statement is false. The null hypothesis will either be true or it​ won't be​ - there is no probability associated with this fact. A​ p-value is the probability of observing a sample mean​ (for example) that we did or something more unusual just by chance if the null hypothesis is false. This statement is false. While there is a chance that the null hypothesis is​ true, a​ p-value tells us the probability of observing a sample mean​ (for example) that we did or something more unusual. This statement is true. This statement is false. The null hypothesis will either be true or it​ won't be true​ - there is no probability associated with this fact. A​ p-value is the probability of observing a sample mean​ (for example) that we did or something more unusual just by chance if the null hypothesis is true. This statement is false. A​ p-value is the probability that the null hypothesis is false.

This statement is false. The null hypothesis will either be true or it​ won't be true​ - there is no probability associated with this fact. A​ p-value is the probability of observing a sample mean​ (for example) that we did or something more unusual just by chance if the null hypothesis is true.

A p-value is the probability of accepting the null hypothesis. This statement is false. We never accept the null hypothesis no matter what the p-value is. A p-value is the probability of observing a sample mean (for example) or something more unusual just by chance if the null hypothesis is false. This statement is false. We never accept the null hypothesis no matter what the p-value is. A p-value is the probability of observing a sample mean (for example) or something more unusual just by chance if the null hypothesis is true. This statement is true. This statement is false. A p-value is the probability of rejecting the null hypothesis. This statement is false. While we may accept the null hypothesis as true depending on what the p-value is, a p-value is the probability of observing a sample mean (for example) that we did or something more unusual just by chance.

This statement is false. We never accept the null hypothesis no matter what the p-value is. A p-value is the probability of observing a sample mean (for example) or something more unusual just by chance if the null hypothesis is true.

A​ p-value is the probability of accepting the null hypothesis. This statement is true. This statement is false. A​ p-value is the probability of rejecting the null hypothesis. This statement is false. We never accept the null hypothesis no matter what the​ p-value is. A​ p-value is the probability of observing a sample mean​ (for example) that we did or something more unusual just by chance if the null hypothesis is true. This statement is false. While we may accept the null hypothesis as true depending on what the​ p-value is, a​ p-value is the probability of observing a sample mean​ (for example) that we did or something more unusual just by chance. This statement is false. We never accept the null hypothesis no matter what the​ p-value is. A​ p-value is the probability of observing a sample mean​ (for example) that we did or something more unusual just by chance if the null hypothesis is false.

This statement is false. We never accept the null hypothesis no matter what the​ p-value is. A​ p-value is the probability of observing a sample mean​ (for example) that we did or something more unusual just by chance if the null hypothesis is true.

The smaller the p-value, the more likely that our evidence has significance (meaningful results). True. Smaller p-values indicate that the probability of our evidence being due to chance is unlikely assuming the null is valid. Thus, smaller p-values provide more evidence to reject the null hypothesis. False. Smaller p-values indicate an unlikely probability of gathering our evidence. Thus, smaller p-values provide more evidence to support the null hypothesis.

True. Smaller p-values indicate that the probability of our evidence being due to chance is unlikely assuming the null is valid. Thus, smaller p-values provide more evidence to reject the null hypothesis.

The​ vice-president of operations wondered if the average strength of wire cables was different between those produced at the​ company's plant in a rural location and those produced in the​ company's plant located in a large city. The VP performed a hypothesis test and obtained a​ p-value of 0.02. The power of the test was 0.80. He decided to reject the null hypothesis. What type of error could the VP have​ made? Calculation error. Type I error. Measurement error. Type II error.

Type I error.

A quality control technician wanted to construct a confidence interval for the average weight of tablets of a nutritional supplement being produced at a​ company's manufacturing facility. The technician selected a simple random sample of 1500​ tablets, and a​ 90% confidence interval for the average weight of all tablets was determined to be​ (3412 mg., 3454​ mg.). Which of the following is a correct interpretation of this​ interval? We can be​ 90% confident that​ 90% of all tablets have weights between 3412 and 3454 milligrams. 90% of all tablets have weights between 3412 and 3454 milligrams. We can be​ 90% confident that the average weight of the tablets in this sample is between 3412 and 3454 milligrams. We can be​ 90% confident that the average weight of all tablets is between 3412 and 3454 milligrams.

We can be​ 90% confident that the average weight of all tablets is between 3412 and 3454 milligrams.

When is a​ t-test performed instead of a​ z-test? When the population standard deviation is known. When the population standard deviation is not known. When the sample standard deviation is not known. When researchers are pretty certain the null hypothesis will be rejected

When the population standard deviation is not known.

When are conclusions said to be​ "statistically significant"? When neither a Type I Error nor a Type II Error have been made. When the power is high. When the​ p-value is less than a given significance level. When the significance level is 0.05 or less. When the​ p-value is greater than a given significance level.

When the​ p-value is less than a given significance level.

The probability of observing the experiment​ result, a sample​ mean, for​ example, or something more unusual just by chance if the null hypothesis is true is the definition of​ _____________. the alternative hypothesis. a confidence interval. a p-value. the test statistic.

a p-value.

A study was conducted in order to estimate μ, the mean number of weekly hours that U.S. adults use computers at home. Suppose a random sample of 81 U.S. adults gives a mean weekly computer usage time of 8.5 hours and that from prior studies, the population standard deviation is assumed to be σ = 3.6 hours. A similar study conducted a year earlier estimated that μ, the mean number of weekly hours that U.S. adults use computers at home, was 8 hours. We would like to test (at the usual significance level of 5%) whether the current study provides significant evidence that this mean has changed since the previous year. Using a 95% confidence interval of (7.7, 9.3), our conclusion is that: the current study does provide significant evidence that the mean number of weekly hours has changed over the past year, since 8 falls outside the confidence interval. the current study does not provide significant evidence that the mean number of weekly hours has changed over the past year, since 8 falls outside the confidence interval. the current study does provide significant evidence that the mean number of weekly hours has changed over the past year, since 8 falls inside the confidence interval. the current study does not provide significant evidence that the mean number of weekly hours has changed over the past year, since 8 falls inside the confidence interval. None of the above. The only way to reach a conclusion is by finding the p-value of the test.

the current study does not provide significant evidence that the mean number of weekly hours has changed over the past year, since 8 falls inside the confidence interval.

Food inspectors inspect samples of food products to see if they are safe. This can be thought of as a hypothesis test with the following hypotheses. H0: the food is safe Ha: the food is not safe The following is an example of what type of error? The sample suggests that the food is safe, but it actually is not safe. type I type II not an error

type II The statement describes a situation where we fail to reject a false null hypothesis. This is a Type II error