Question 1

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 of data comes from a specific distribution. The runs test is used to detect departures from randomness in a sequence of data, but does not test against a specific distribution. The binomial test is used to test a proportion or percentage against a known population value, and does not test against a specific distribution. The Mann-Whitney U test is used to compare two independent groups and is not appropriate for testing goodness-of-fit.

Question 2

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

The runs test is specifically designed to test whether a series of observations or data points are arranged in a random, non-patterned order or sequence. The other tests listed (Mann-Whitney U test, sign test, binomial test) are not intended to evaluate randomness or sequential order.

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 compare the variances of two populations. The z test and t test are used to compare means of populations, and the paired samples test is used to compare means of two related samples.

Question 4

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

If the null hypothesis cannot be rejected, this means that there is not enough evidence to suggest that the distribution significantly deviates from the normal distribution. Therefore, the best choice is B.

Question 5

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 the F test in this case are that the two populations have equal variance (null hypothesis) versus they do not have equal variance (alternative hypothesis). The notation for this can be written as H₀:σ₁² = σ₂² versus H₁:σ₁² ≠ σ₂².

Question 6

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 when testing hypotheses about one mean is equal to the sample size minus one (n-1).

Question 7

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 there is no significant difference between the variances of the two populations. In such a case, it is appropriate to use the t-test with equal variances assumed (i.e., the pooled t-test). Therefore, option B is the best choice.

Question 8

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 is n-1, where n is the number of pairs of observations. This is because there is one less degree of freedom due to the constraint that the differences between the pairs must sum to zero. Option A is incorrect because it is too vague and does not provide a specific value for the degrees of freedom. Option C is incorrect because it includes values for S1, U1, B11, and B12 which are not defined in the question. Option D is incorrect because it does not properly account for the constraint that the differences between the pairs must sum to zero.

Question 9

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 10

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 (0.248), so the null hypothesis cannot be rejected.

Question 11

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 differences in the location of two populations based on observations from two independent samples when the variable is measured on an ordinal scale. The other options are not appropriate for this type of analysis. The Kolmogorov-Smirnov one-sample test is used to test for normality of a distribution or to compare a sample distribution to a theoretical distribution. The runs test is used to test for randomness in a sequence of data. The binomial test is used to test if the proportion of successes in a sample differs from a known proportion.

Question 12

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

In the parametric case of means for two independent samples, the null hypothesis states that the means of the two populations are equal, while the alternative hypothesis states that they are not equal. Hence, Option A represents the correct form of hypotheses for this scenario. Option B represents the equal variances case, Option C represents a one-sample mean test, and Option D represents a proportion test.

Question 13

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 answer of The ________ is a frequency distribution that...

Question 14

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 since it uses the known population standard deviation in its calculation. On the other hand, a t test uses the estimated standard deviation from the sample, which is not necessary if the population standard deviation is known. Therefore, option A is the best choice. The F test is used to compare variances of two populations and is not relevant in this scenario.

Question 15

Accepted Answer

The Kolmogorov-Smirnov one-sample test uses the test statistic K, which is the maximum absolute difference between the cumulative distribution function of the sample and the theoretical cumulative distribution function. Therefore, the correct formula for K is K = Max | A_i - O_i |.

Question 16

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 17

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 correct choice for the hypotheses for testing whether the mean familiarity rating exceeds 4.0 is C. This is because we are interested in testing whether the mean value is greater than a specific value (i.e., 4.0), and the null hypothesis (H₀) represents the idea that the mean value is less than or equal to the neutral value of 4.0, while the alternative hypothesis (H₁) represents the idea that the mean value is greater than 4.0.

Question 18

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 not skewed to the left or right, it is symmetric around its mean.

Question 19

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.

Question 20

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.

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

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

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

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 ________.

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

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

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

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

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.

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

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.

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

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 ________.

Which statement is not true concerning the t distribution?

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

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