Question 1

The degrees of freedom for the t statistic to test hypotheses about one mean are ________. A)n B)n - 1 C)n₁ + n₂ D)n₁ +n₂ - 2

Accepted Answer

The degrees of freedom for the t statistic to test hypotheses about one mean is equal to the sample size minus one, which is represented by n - 1.

Question 2

A one-sample nonparametric goodness-of-fit test to determine whether the observations for a particular variable could reasonably have come from a particular distribution is the ________.
A)Kolmogorov-Smirnov one-sample test
B)runs test
C)binomial test
D)Mann-Whitney U test

Accepted Answer

The Kolmogorov-Smirnov one-sample test is specifically designed to test whether a sample comes from a particular distribution. The runs test is used to test for randomness in data, the binomial test is used to test the probability of success in a binomial experiment, and the Mann-Whitney U test is used to compare two independent groups.

Question 3

The ________ is a statistical test of the equality of the variances of two populations.
A)z test
B)t test
C)paired samples test
D)F test

Accepted Answer

The F test is used to test the equality of variances of two populations. The z test is used to test the mean of a population with a known variance, the t test is used to test the mean of a population with an unknown variance, and the paired samples test is used to compare means of two related samples.

Question 4

If the probability of F is greater than the significance level α,________ and ________ should be used. A)H₀is rejected;t based on "equal variances not assumed" B)H₀is not rejected;t based on "equal variances assumed" C)H₀is rejected;t based on "equal variances assumed" D)H₀is not rejected;t based on "equal variances not assumed"

Accepted Answer

If the probability of F is greater than the significance level α, it means that the variances of the two samples are likely equal. Therefore, we can use the t-test assuming equal variances, which is the option presented in choice B.

Question 5

Which statement is not true concerning the t distribution? A)Compared to the normal distribution,the t distribution has more area in the tails and less in the center. B)As the number of degrees of freedom increases,the t distribution approaches the normal distribution. C)The t distributions are skewed to the left. D)The population variance is unknown and is estimated by the sample variance s².

Accepted Answer

The t distribution is symmetric and not skewed to the left. Option A is true because the t distribution has more area in the tails and less in the center than the normal distribution. Option B is also true because as the number of degrees of freedom increase, the t distribution approaches the normal distribution. Option D is also true because the population variance is unknown and is estimated by the sample variance.

Question 6

The F test of sample variance may be performed if it is not known whether the two populations have equal variance.In this case the hypotheses are ________. A)H₀:μ₁ = μ₂ H₁:μ₁ ≠ μ₂ B)H₀:σ₁² = σ₂² H₁:σ₁² ≠ σ₂² C)H₀:μ ≤ 4.0 H₁:μ > 4.0 D)H₀: π₁ = π₂ H₁: π₁ ≠ π₂

Accepted Answer

The hypotheses for F test of sample variance are related to the population variances, not the population means or proportions. Therefore, options A, C, and D are incorrect. Option B presents the correct hypotheses for F test of sample variance, where the null hypothesis is that the population variances are equal and the alternative hypothesis is that they are not equal.

Question 7

When the difference in the location of two populations is to be compared based on observations from two independent samples,and the variable is measured on an ordinal scale,the ________ can be used.
A)Kolmogorov-Smirnov one-sample test
B)runs test
C)binomial test
D)Mann-Whitney U test

Accepted Answer

The Mann-Whitney U test is used to compare the location of two populations based on observations from two independent samples when the variable is measured on an ordinal scale. The test is non-parametric, meaning it does not assume normality of data, and it tests whether one sample tends to have higher or lower values than the other sample. The other options are not suitable for this type of comparison on ordinal data.

Question 8

The ________ is a frequency distribution that depends upon two sets of degrees of freedom,the degrees of freedom in the numerator and the degrees of freedom in the denominator.
A)t distribution
B)Z statistic
C)chi-square distribution
D)none of the above

Accepted Answer

The F-distribution, not listed among the choices, is the frequency distribution that depends on two sets of degrees of freedom: one for the numerator and one for the denominator.

Question 9

Which of the following tests is not a non-parametric one-sample test?
A)Kolmogorov-Smirnov one-sample test
B)runs test
C)binomial test
D)Mann-Whitney U test

Accepted Answer

The Mann-Whitney U test is a non-parametric test for comparing two independent samples, not a one-sample test. The other options (Kolmogorov-Smirnov one-sample test, runs test, and binomial test) are indeed non-parametric one-sample tests.

Question 10

Accepted Answer

The Kolmogorov-Smirnov one-sample test uses the test statistic K, which is the maximum absolute difference between the empirical distribution function of the sample and the theoretical distribution function. Therefore, the correct formula is K = Max |F(x) - G(x)|, where F(x) is the empirical distribution function of the sample and G(x) is the theoretical distribution function. Choice C is the formula that correctly represents K.

Question 11

For the parametric case involving the means of paired samples,the null and alternative hypotheses are ________. A)H₀:μ₁ = μ₂ H₁:μ₁ ≠ μ₂ B)H₀:σ₁² = σ₂² H₁:σ₁² ≠ σ₂² C)H₀:μ_D = 0 H₁:μ_D ≠ 0 D)H₀: π₁ = π₂ H₁: π₁ ≠ π₂

Accepted Answer

For the parametric case involving the means of paired samples, the null hypothesis typically states that the mean difference between the paired samples is zero (H0: μD = 0), and the alternative hypothesis states that the mean difference is not zero (H1: μD ≠ 0). This is because paired samples are used to compare two means from the same group under different conditions or at different times, and the interest is in the difference between these means.

Question 12

Suppose we wanted to test the hypothesis that the mean familiarity rating exceeds 4.0,the neutral value on a seven-point scale.The hypotheses may be formulated as ________. A)H₀:μ₁ = μ₂ H₁:μ₁ ≠ μ₂ B)H₀:σ₁² = σ₂² H₁:σ₁² ≠ σ₂² C)H₀:μ ≤ 4.0 H₁:μ > 4.0 D)H₀: π₁ = π₂ H₁: π₁ ≠ π₂

Accepted Answer

The hypothesis should be formulated in terms of the population mean (μ) and whether it is greater than, less than, or equal to the neutral value of 4.0 on the familiarity rating scale. Therefore, option C is the correct choice as it states the null hypothesis as μ ≤ 4.0 and the alternative hypothesis as μ > 4.0.

Question 13

If the population standard deviation was assumed to be known,rather than estimated from the sample,a ________ would be appropriate rather than a ________.
A)z test;t test
B)t test;F test
C)t test;z test
D)z test;F test

Accepted Answer

If the population standard deviation is assumed to be known, a z test would be appropriate rather than a t test. The z test is used when the standard deviation of the population is known, while the t test is used when the standard deviation of the population is unknown and must be estimated from the sample. The F test is used to compare the variances of two or more populations, which is not relevant to this scenario.

Question 14

In the context of the Internet usage example,suppose we wanted to test whether the probability of observing a K value of .222,as determined by the normalized z statistic,is 0.103.Because this is more than the significance level of 0.05,the null hypothesis cannot be rejected.What do the results mean?
A)The distribution of the Internet usage does deviate significantly from the normal distribution.
B)The distribution of the Internet usage does not deviate significantly from the normal distribution.
C)The proportion of users for males and for females is not significantly different for the two samples.
D)The proportion of users for males and for females is significantly different for the two samples.

Accepted Answer

The fact that the null hypothesis cannot be rejected means that we do not have enough evidence to support the alternative hypothesis, which in this case would be that the distribution of Internet usage deviates significantly from the normal distribution. Therefore, we can conclude that the distribution of Internet usage does not deviate significantly from the normal distribution.

Question 15

A ________ is a test conducted by determining whether the order or sequence in which observations are obtained is random.
A)Mann-Whitney U test
B)sign test
C)binomial test
D)runs test

Accepted Answer

A runs test is specifically designed to test for randomness in the sequence or order of observations. The other tests listed are used for different types of hypothesis testing.

Question 16

A Kolmogorov-Smirnov one-sample test was conducted.The largest absolute difference between the observed and normal distribution was K = 0.222.The sample size was only 30 therefore,the approximate formula was used and the critical value for K was 0.248.Because the calculated value of K is ________ than the critical value,the null hypothesis ________ be rejected.
A)smaller;cannot
B)larger;cannot
C)smaller;can
D)larger;can

Accepted Answer

The calculated value of K (0.222) is smaller than the critical value for K (0.248). Therefore, the null hypothesis cannot be rejected.

Question 17

The degrees of freedom for the t statistic to test the hypothesis about two independent samples is ________. A)n B)n - 1 C)n₁ + n₂ D)n₁ +n₂ - 2

Accepted Answer

The degrees of freedom for the t statistic to test the hypothesis about two independent samples is given by: df = (s1^2/n1 + s2^2/n2)^2 / {[(s1^2/n1)^2/(n1 - 1)] + [(s2^2/n2)^2/(n2 - 1)]}. This simplifies to df = n1 + n2 - 2 when the sample sizes are equal and the population variances are assumed to be equal. Therefore, the correct choice is D, n1S1^2/U1B1 + n2S2^2/U2B2 - 2.

Question 18

The degrees of freedom for the t statistic to test hypotheses about paired samples are ________. A)n B)n - 1 C)n₁ + n₂ D)n₁ + n₂ - 2

Accepted Answer

The degrees of freedom for the t statistic to test hypotheses about paired samples are calculated as n - 1, where n is the number of pairs. This accounts for the estimation of one parameter (the mean difference) from the sample data.

Question 19

In the parametric case of means for two independent samples,the hypotheses take which form? A)H₀:μ₁ = μ₂ H₁:μ₁ ≠ μ₂ B)H₀:σ₁² = σ₂² H₁:σ₁² ≠ σ₂² C)H₀:μ ≤ 4.0 H₁:μ > 4.0 D)H₀: π₁ = π₂ H₁: π₁ ≠ π₂

Accepted Answer

The hypotheses in the parametric case of means for two independent samples take the form of comparing the means of two populations. In this case, the null hypothesis states that the means are equal (μ1 = μ2) and the alternative hypothesis states that the means are not equal (μ1 ≠ μ2). Option A correctly represents this format, while options B, C, and D represent different types of hypotheses, such as hypothesis testing for variances (option B), one-sample means (option C), and proportions (option D).

Question 20

For the parametric case,involving proportions for two independent samples,the null and alternative hypotheses are ________. A)H₀:μ₁ = μ₂ H₁:μ₁ ≠ μ₂ B)H₀:σ₁² = σ₂² H₁:σ₁² ≠ σ₂² C)H₀:μ ≤ 4.0 H₁:μ > 4.0 D)H₀: π₁ = π₂ H₁: π₁ ≠ π₂

Accepted Answer

For proportions in two independent samples, the hypotheses compare the population proportions (π1 and π2), not means or standard deviations.

Quiz 15: Frequency Distribution,cross-Tabulation,and Hypothesis Testing

The degrees of freedom for the t statistic to test hypotheses about one mean are ________.

A one-sample nonparametric goodness-of-fit test to determine whether the observations for a particular variable could reasonably have come from a particular distribution is the ________.

The ________ is a statistical test of the equality of the variances of two populations.

If the probability of F is greater than the significance level α, and should be used.

Which statement is not true concerning the t distribution?

The F test of sample variance may be performed if it is not known whether the two populations have equal variance.In this case the hypotheses are ________.

When the difference in the location of two populations is to be compared based on observations from two independent samples,and the variable is measured on an ordinal scale,the ________ can be used.

The ________ is a frequency distribution that depends upon two sets of degrees of freedom,the degrees of freedom in the numerator and the degrees of freedom in the denominator.

Which of the following tests is not a non-parametric one-sample test?

The test statistic used in the Kolmogorov-Smirnov one-sample test is ________.

For the parametric case involving the means of paired samples,the null and alternative hypotheses are ________.

Suppose we wanted to test the hypothesis that the mean familiarity rating exceeds 4.0,the neutral value on a seven-point scale.The hypotheses may be formulated as ________.

If the population standard deviation was assumed to be known,rather than estimated from the sample,a would be appropriate rather than a .

In the context of the Internet usage example,suppose we wanted to test whether the probability of observing a K value of .222,as determined by the normalized z statistic,is 0.103.Because this is more than the significance level of 0.05,the null hypothesis cannot be rejected.What do the results mean?

A ________ is a test conducted by determining whether the order or sequence in which observations are obtained is random.

The degrees of freedom for the t statistic to test the hypothesis about two independent samples is ________.

The degrees of freedom for the t statistic to test hypotheses about paired samples are ________.

In the parametric case of means for two independent samples,the hypotheses take which form?

For the parametric case,involving proportions for two independent samples,the null and alternative hypotheses are ________.