Complete the following mcq:
1. The null hypothesis always states:
a. A hypothesized value for a population parameter.
b. That a population parameter is equal to a hypothesized value.
c. That a population parameter is less than or equal to a hypothesized value.
d. That a population parameter is greater than or equal to a hypothesized value.
2. Which of the following statements is true about the alternate hypothesis?
a. It is accepted if the null hypothesis is rejected.
b. It will always contain the equal sign.
c. It is rejected if the null hypothesis is true.
d. It is accepted if the null hypothesis is accepted.
3. Which of the following statements is true about the level of significance?
a. It is a probability.
b. It can be any value between 0 and 1.
c. It is the likelihood of rejecting the null hypothesis when it is true.
d. All of the above.
4. A Type I error is
a. Calculated from sample information.
b. A probability determined from the test statistic.
c. The probability of rejecting the null hypothesis when it is true.
d. The probability of accepting the null hypothesis when it is false.
5. The critical value is
a. Calculated from sample information.
b. Is always positive.
c. The point that divides the acceptance region from the rejection region.
d. A probability determined from the test statistic.
6. To conduct a one sample test of means and use the z distribution as the test statistic, we need
a. To know the population mean.
b. To know the population standard deviation.
c. n to be less than 5.
d. Both a and b are correct.
7. A p-value is the
a. Same as the population proportion.
b. Same as the significance level.
c. Fraction of the population that has a particular characteristic.
d. Probability of finding a value of the test statistic this extreme when the null hypothesis is true.
8. A Type II error occurs when we
a. Accept the null hypothesis when it is false.
b. Reject the alternate hypothesis when it is true.
c. Reject the null hypothesis when it is false.
d. Accept the null hypothesis when it is true.
9. Which of the following statements are correct when deciding whether to use the z or the t distribution?
a. Use z in a test of proportions when and nπ and n(1 - π) are greater than or equal to 5.
b. Use z when we have a normal population and we know the standard deviation.
c. Use t when the population is normal and the population standard deviation is not known
d. All of the above statements are correct.
10. For H0: μ = 10, α = 0.05, using a z-statistic, and = 12, σ = 4, n = 16,
a. The null hypothesis is accepted.
b. Fail to reject the null hypothesis.
c. Reject the null hypothesis.
d. Reject the alternative hypothesis.
1. In a two-sample test of means for independent samples, the equal sign always appears in the
a. Null hypothesis.
b. Alternate hypothesis.
c. Upper tail of the test statistic.
d. Lower tail of the test statistic.
2. In a two-sample test of means for independent samples, we use the z distribution when
a. The two population standard deviations are equal.
b. Both populations have at least 4000 observations.
c. Both population standard deviations are known.
d. nπ and n(1-π) are both greater than 5.
3. A random sample of 10 observations is selected from the first normal population and 8 from the second normal population. For the hypothesis, H0: μ1 ≤ μ2, what is the number of degrees of freedom?
a. 18
b. 17
c. 16
d. 9
4. A random sample of 10 observations is selected from the first normal population and 8 from the second normal population. For the hypothesis, H0: μ1 ≤ μ2, (.01 significance level), what is (are) the critical value(s)? (Population standard deviations are unknown).
a. 2.583
b. -2.921, 2.921
c. -2.583, 2.583
d. -2.583, 2.921
5. When testing a hypothesis of the means for independent populations (population standard deviations unknown), what should be true?
a. nπ and n(1-π) are both greater than 5.
b. Both populations are normally distributed.
c. The samples sizes selected from each population must be equal.
d. Both B and C
6. To conduct a test of means for two independent populations, which of the following is required?
a. The z-statistic is the test statistic.
b. The t-statistic is the test statistic.
c. nπ and n (1 - π) must be 5.
d. Sampling from the two populations must be random.
7. Another way to state the null hypothesis: H0: μ1 = μ2, is
a. H0: μ1 ≤ μ2
b. H0: μ1 - μ2 = 0
c. H0: μ1 ≥ μ2
d. H0: μ1 - μ2 ≠ 0
8. To conduct a test of hypothesis for dependent populations, we assume that
a. The distribution of the difference between the sampled paired observations follows the normal distribution.
b. Both samples are at least 30.
c. The samples are unrelated.
d. nπ and n(1-π) are both greater than 5.
9. When conducting a test of hypothesis for dependent samples, which of the following is true?
a. The sample size should be at least 30 pairs of observations.
b. The significance level is more than .05.
c. The p-value is more than .10.
d. None of the above.
10. Which of the following is necessary to determine a p-value?
a. Knowledge of whether the test is one-tailed or two-tailed.
b. The value of the test statistic.
c. The level of significance.
d. Both A and B