BA5106
STATISTICS FOR MANAGEMENT
UNIT-III- TESTING OF HYPOTHESIS-PARAMETRIC TESTS
MULTI CHOICE QUESTIONS
1.A _______ is a statement about the population parameter
(A) Statistical Hypothesis
(B) Null Hypothesis
(C) Alternative Hypothesis
(D) Hypothesis
2. ________is a procedure that helps us to ascertain the likelihood of hypothesis population parameter being correct by making use of the sample statistic
(A) Statistical Hypothesis
(B) Null Hypothesis
(C) Test of Hypothesis
(D) Alternative Hypothesis
3. The statistical hypothesis that is set up for testing a hypothesis is known as ________
(A) \choice Statistical Hypothesis
(B) Null Hypothesis
(C) Test of Hypothesis
(C) Alternative Hypothesis
4. _______is the hypothesis which is to be tested for possible rejection under the assumption it is true
(A) Statistical Hypothesis
(B) Test of Hypothesis
(C) Null Hypothesis
(D) Alternative Hypothesis
5. The negation of Null hypothesis is called the __________
(A) Statistical Hypothesis
(B) Test of Hypothesis
(C) Alternative Hypothesis
(D) Null Hypothesis
6. The rejection region may be reresented by a portion of area on each of the two sides or by only one side of the normal curve and correspondingly the test is known as _________
(A) One tailed test
(B) Two tailed test
(C) Two side test
(D) Not one tailed test
7. The Standard deviation of population is __________
(A) $\mu$
(B) $\sigma$
(C) P
(D) N
8. Test of significance of single mean-large samples then $S.E(\bar{x})= $ _______ when the standard deviation $\sigma$ of population is known
(A) $\frac{\sigma}{\sqrt{n+1}}$
(B) $\frac{\sigma}{\sqrt{n-1}}$
(C) $\frac{\sigma}{\sqrt{n}}$
(D) $\frac{\sigma}{\sqrt{n}+1}$
9. Test of significance of single mean-large samples then $S.E(\bar{x})=$ ______ when the standard deviation $\sigma$ of population is unknown
(A) $\frac{s}{\sqrt{n}+1}$
(B) $\frac{s}{\sqrt{n+1}}$
(C) $\frac{s}{\sqrt{n-1}}$
(D) $\frac{s}{\sqrt{n}}$
10. The sample size $n<30$ the student's t-statistic is defined as t=______
(A) $\frac{\bar{x} - \mu}{S.E(\bar{x})+1}$
(B) $\frac{\bar{x} \times \mu}{S.E(\bar{x})}$
(C) $\frac{\bar{x}+\mu}{S.E(\bar{x})}$
(D) $\frac{\bar{x}-\mu}{S.E(\bar{x})}$
11. Test of significance of Single Proportion-large samples then $S.E(p)=__________$ when the n is the sample size and P is population proportion
(A) $\sqrt{\frac{P(1+P)}{n}}$
(B) $\sqrt{\frac{P(100-P)}{n}}$
(C) $\sqrt{\frac{P(1-P)}{n}}$
(D) $\sqrt{\frac{P(100+P)}{n}}$
12. Test of significance of Single Proportion-large samples then $S.E(p)=_________$ when the n is the sample size and P is population percentage
(A) $\sqrt{\frac{P(1+P)}{n}}$
(B) $\sqrt{\frac{P(1-P)}{n}}$
(C) $\sqrt{\frac{P(100+P)}{n}}$
(D) $\sqrt{\frac{P(100-P)}{n}}$
13. Test of significance of Difference between two sample proportion for large samples then $S.E(p_1-p_2)=_______$ when the population proportion $P_1$ and $P_2$ are known
(A) $\sqrt{\frac{P_1Q_1}{n_1}+\frac{P_2Q_2}{n_2}}$
(B) $\sqrt{\frac{P_1Q_1}{n_1} -\frac{P_2Q_2}{n_2}}$
(C) $\sqrt{\frac{P_1Q_1}{n_1} \times \frac{P_2Q_2}{n_2}}$
(D) $\sqrt{\frac{P_1Q_1}{n_1} / \frac{P_2Q_2}{n_2}}$
14. Test of significance of Difference between two sample proportion for large samples then $S.E(p_1-p_2)=_______$ when the population proportion $P_1$ and $P_2$ are unknown but sample proportion $p_1$ and $p_2$ are known
(A) $\sqrt{\frac{p_1q_1}{n_1} -\frac{p_2q_2}{n_2}}$
(B) $\sqrt{\frac{p_1q_1}{n_1}+\frac{p_2q_2}{n_2}}$
(C) $\sqrt{\frac{p_1q_1}{n_1} \times \frac{p_2q_2}{n_2}}$
(D) $\sqrt{\frac{p_1q_1}{n_1} / \frac{p_2q_2}{n_2}}$
15. A sample is said to be a small sample if the size of the sample is _________
(A) $n \geq 30$
(B) $n=30$
(C) $n>30$
(D) $n<30$
16. A sample is said to be a large sample if the size of the sample is____________
(A) $n \leq 30$
(B) $n=30$
(C) $n>30$
(D) $n<30$
17. Test of significance of single mean-samll samples then $S.E(\bar{x})=$ when the standard deviation s and n size of sample
(A) $\frac{s}{\sqrt{n}+1}$
(B) $\frac{s}{\sqrt{n+1}}$
(C) $\frac{s}{\sqrt{n}}$
(D) $\frac{s}{\sqrt{n-1}}$
18. Test of significance of paired t-test then $S.E(\bar{x_1}-\bar{x}_2)=$______
(A) $\frac{S}{\sqrt{n}+1}$
(B) $\frac{S}{\sqrt{n}}$
(C) $\frac{S}{\sqrt{n+1}}$
(D) $\frac{S}{\sqrt{n-1}}$
19. Test of signification of difference between two means-large samples then $S.E(\bar{x_1}-\bar{x_2})=$_________ when the population standard deviation $\sigma_1$ and $\sigma_2$ are known
(A) $\sqrt{\frac{\sigma_1^2}{n_1}+\frac{\sigma_2^2}{n_2}}$
(B) $\sqrt{\frac{\sigma_1^2}{n_1}-\frac{\sigma_2^2}{n_2}} $
(C) $\sqrt{\frac{\sigma_1^2}{n_1} \times \frac{\sigma_2^2}{n_2}} $
(D) $\sqrt{\frac{\sigma_1^2}{n_1} / \frac{\sigma_2^2}{n_2}} $
20. Test of signification of difference between two means-large samples then Z= _________ when the population standard deviation $\sigma_1$ and $\sigma_2$ are known
(A) $\frac{\bar{x_1} / \bar{x_2}}{S.E(\bar{x_1}-\bar{x}_2} $
(B) $\frac{\bar{x_1}-\bar{x_2}}{S.E(\bar{x_1}-\bar{x}_2} $
(C) $\frac{\bar{x_1}+\bar{x_2}}{S.E(\bar{x_1}-\bar{x}_2} $
(D) $\frac{\bar{x_1} \times \bar{x_2}}{S.E(\bar{x_1}-\bar{x}_2} $
21. Test of signification of difference between two standard deviation -large samples then $S.E(s_1-s_2)=$________ when the population standard deviation $\sigma_1$and $\sigma_2$ are known
(A) $\sqrt{\frac{\sigma_1^2}{2n_1}-\frac{\sigma_2^2}{2n_2}} $
(B) $\sqrt{\frac{\sigma_1^2}{2n_1}+\frac{\sigma_2^2}{2n_2}}$
(C) $\sqrt{\frac{\sigma_1^2}{n_1} \times \frac{\sigma_2^2}{n_2}} $
(D) $\sqrt{\frac{\sigma_1^2}{n_1} / \frac{\sigma_2^2}{n_2}} $
22. Test of signification of difference between two standard deviation -large samples then $Z=$________ when the population standard deviation $\sigma_1$and $\sigma_2$ are known
(A) $\frac{s_1 / s_2}{S.E(s_1-s_2)}$
(B) $\frac{s_1 \times s_2}{S.E(s_1-s_2)}$
(C) $\frac{s_1 +s_2}{S.E(s_1-s_2)}$
(D) $\frac{s_1-s_2}{S.E(s_1-s_2)}$
23.Test of signification of difference between two standard deviation -large samples then $S.E(s_1-s_2)=$________ when the population standard deviation $\sigma_1$and $\sigma_2$ are unknown
(A) $\sqrt{\frac{s_1^2}{2n_1}-\frac{s_2^2}{2n_2}} $
(B) $\sqrt{\frac{s_1^2}{n_1} \times \frac{s_2^2}{n_2}} $
(C) $\sqrt{\frac{s_1^2}{n_1} / \frac{s_2^2}{n_2}} $
(D) $\sqrt{\frac{s_1^2}{2n_1}+\frac{s_2^2}{2n_2}}$
24. Test of signification of difference between two standard deviation -large samples then $Z=$ _________ when the population standard deviation $\sigma_1$and $\sigma_2$ are known
(A) $\frac{s_1 / s_2}{S.E(s_1-s_2)}$
(B) $\frac{s_1 \times s_2}{S.E(s_1-s_2)}$
(C) $\frac{s_1-s_2}{S.E(s_1-s_2)}$
(D) $\frac{s_1 +s_2}{S.E(s_1-s_2)}$
25. Test of signification of difference between two means -small samples then $ S^2=$_________ be the unbiased estimate of common population variance based on both the samples
(A) $\frac{n_1s_1^2+n_2s_2^2}{n_1+n_2-2}$
(B) $\frac{n_1s_1^2-n_2s_2^2}{n_1+n_2-2}$
(C) $\frac{n_1s_1^2 \times n_2s_2^2}{n_1+n_2-2}$
(D) $\frac{n_1s_1^2 / n_2s_2^2}{n_1+n_2-2}$
26. Test of signification of difference between two means -small samples then $ S.E(\bar{x_1}-\bar{x_2})=$_________
(A) $S / \sqrt{\frac{1}{n_1}+\frac{1}{n_2}}$
(B) $S\times \sqrt{\frac{1}{n_1}+\frac{1}{n_2}}$
(C) $S + \sqrt{\frac{1}{n_1}+\frac{1}{n_2}}$
(D) $S - \sqrt{\frac{1}{n_1}+\frac{1}{n_2}}$
27. Test of signification of difference between two means -small samples then $ t=$_________
(A) $ \frac{\bar{x_1}-\bar{x_2}}{S.E(\bar{x_1}-\bar{x_2})}$
(B) $ \frac{\bar{x_1} \times \bar{x_2}}{S.E(\bar{x_1}-\bar{x_2})}$
(C) $ \frac{\bar{x_1}+\bar{x_2}}{S.E(\bar{x_1}-\bar{x_2})}$
(D) $ \frac{\bar{x_1} / \bar{x_2}}{S.E(\bar{x_1}-\bar{x_2})}$
28. _________ refers to a test of hypothesis concerning two variance derived from two samples
(A) T-test
(B) F test
(C) Z -test
(D) $\psi^2$-test
29. Test of hypothesis about the variance of two population $F=$________
(A) $\frac{\hat{\sigma_1}^{2}}{\hat{\sigma_2}^2}$
(B) $\hat{\sigma_1}^{2} \times \hat{\sigma_2}^{2}$
(C) $ \hat{\sigma_1}^{2} +\hat{\sigma_2}^{2} $
(D) $\hat{\sigma_1}^{2} - \hat{\sigma_2}^{2} $
30. The variance ratio is obtained by dividing the variance between the samples by the variance within the samples.This ratio forms the test ___________
(A) T-statistic
(B) F statistic
(C) Z -statistic
(D) $\psi^2$- statistic
\end{oneparchoices}
31. Sum of squares of variance amongst the columns $SSC=_______$ it is the sum of the squares of deviation between the columns or group means and the grand mean
(A) $ r \sum (\bar{x_j} / \bar{x})^2 $
(B) $ r \sum (\bar{x_j} \times \bar{x})^2 $
(C) $ r \sum (\bar{x_j}-\bar{x})^2 $
(D) $ r \sum (\bar{x_j}+\bar{x})^2 $
32. Sum of squares of variance amongst the columns $SSE=______$ it is the sum of the squares of variance between individual items and the columns means
(A) $ \sum_i\sum_i (x_{ij} + \bar{x}_j)^2 $
(B) $ \sum_i\sum_i (x_{ij} \times \bar{x}_j)^2 $
(C) $ \sum_i\sum_i (x_{ij} / \bar{x}_j)^2 $
(D) $ \sum_i\sum_i (x_{ij}-\bar{x}_j)^2 $
33. Mean of the square of columns Errors MSE=_______
(A) $ \frac{SSE}{c(r+1)}$
(B) $ \frac{SSE}{c(r-1)}$
(C) $ \frac{SSE}{c(r \times 1)}$
(D) $ \frac{SSE}{c(r)}$
34. Total sum of squares of variance SST=__________
(A) $ \sum_{j}\sum_i x_{ij}^2 - C $
(B) $ \sum_{j}\sum_i x_{ij}^2 / C $
(C) $ \sum_{j}\sum_i x_{ij}^2 + C $
(D) $ \sum_{j}\sum_i x_{ij}^2 \times C $
35. The sum of the square of observation between the individual values and the grand mean $\bar{x}$ then SST=_______
(A) SSC-SSE
(B) SSC+SSE
(C) SSC $\times$ SSE
(D) SSC /SSE
36. The total variance comprise of both the explained and the unexplained variance and defined as total variance=_________
(A) $\frac{SST}{n+1} $
(B) $\frac{SST}{n-1} $
(C) $\frac{SST}{n\times 2} $
(D) $\frac{SST}{n} $
37.The test statistic is the F-value or F-statistic and is defined as F= ________
(A) $MSC \times MSE $
(B) $MSC -MSE $
(C) $MSC +MSE $
(D) $\frac{MSC}{MSE}$
38. Variance amongst columns (Mean square Column ) MSC=______
(A) $ SSC-(c-1)$
(B) $ \frac{SSC}{c-1}$
(C) $ SSC+(c-1) $
(D) $ SSC \times (c-1)$
39. Variance amongst Error (Mean square Error ) MSE=______
(A) $ SSE-c(r-1)$
(B) $ SSC+c(r-1) $
(C) $ \frac{SSE}{c(r-1)}$
(D) $ SSC \times c(r-1)$
40. In a past General Social Survey, a random sample of men and women answered the question “Are you a member of any sports clubs?” Based on the sample data, 95% confidence intervals for the population proportion who would answer “yes” are 0.13 to 0.19 for women and 0.247 to 0.33 for men.Based on these results, you can reasonably conclude that
(A) There is a difference between the proportions of American men and American women who belong to sports clubs.
(B) There is no conclusive evidence of a gender difference in the proportion belonging to sports clubs
(C) At least 16$\%$ of American women belong to sports clubs
(D) At least 25$\%$ of American men and American women belong to sports clubs
41. In hypothesis testing, a Type 2 error occurs when
(A) The null hypothesis is not rejected when the null hypothesis is true
(B) The null hypothesis is rejected when the null hypothesis is true
(C) The null hypothesis is not rejected when the alternative hypothesis is true
(D) The null hypothesis is rejected when the alternative hypothesis is true
42. Null and alternative hypotheses are statements about
(A) it depends - sometimes population parameters and sometimes sample statistics
(B) population parameters
(C) sample parameters
(D) sample statistics.
43. A hypothesis test is done in which the alternative hypothesis is that more than 10% of a population is left-handed. The p-value for the test is calculated to be 0.25. Which statement is correct?
(A) We cannot conclude that more than $10\% $of the population is left-handed
(B) We can conclude that more than $25\%$ of the population is left-handed
(C) We can conclude that more than $10\%$ of the population is left-handed
(D) We can conclude that exactly $25\%$ of the population is left-handed.
44. Which of the following is NOT true about the standard error of a statistic?
(A) The standard error measures, roughly, the average difference between the statistic and the population parameter
(B) The standard error is the estimated standard deviation of the sampling distribution for the statistic
(C) The standard error increases as the sample size(s) increases
(D) The standard error can never be a negative number.
45. A result is called “statistically significant” whenever
(A) The null hypothesis is true
(B) The alternative hypothesis is true
(C) The p-value is larger than the significance level
(D) The p-value is less or equal to the significance level
46. Consider a random sample of 100 females and 100 males. Suppose 15 of the females are left-handed and 12 of the males are left-handed. What is the estimated difference between population proportions of females and males who are left-handed (females - males)? Select the choice with the correct notation and numerical value
(A) $p_1-p_2 =3 $
(B) $ p_1 - p_2 = 0.03 $
(C) $ \hat{p} - \hat{p_2} = 3$
(D) $\hat{p_1} - \hat{p_2} = 0.03$
47. The confidence level for a confidence interval for a mean is
(A) the probability the procedure provides an interval that covers the sample mean
(B) the probability the procedure provides an interval that covers the population mean. }
(C) the probability of making a Type 1 error if the interval is used to test a null hypothesis about the population mean
(D) the probability that individuals in the population have values that fall into the interval.
48. A test of $H_0: \mu = 0$ versus $H_1: \mu > 0$ is conducted on the same population independently by two different researchers. They both use the same sample size and the same value of $\aleph = 0.05$. Which of the following will be the same for both researchers?
(A) The p-value of the test
(B) The value of the test statistic
(C) The power of the test if the true $\mu = 6$.
(D) The decision about whether or not to reject the null hypothesis.
49.A test to screen for a serious but curable disease is similar to hypothesis testing, with a null hypothesis of no disease, and an alternative hypothesis of disease. If the null hypothesis is rejected treatment will be given. Otherwise, it will not. Assuming the treatment does not have serious side effects, in this scenario it is better to increase the probability of:
(A) making a Type 1 error, not providing treatment when it is needed.
(B) making a Type 2 error, providing treatment when it is not needed.
(C) making a Type 1 error, providing treatment when it is not needed.
(D) making a Type 2 error, not providing treatment when it is needed.
50. The average time in years to get an undergraduate degree in computer science was compared for men and women. Random samples of 100 male computer science majors and 100 female computer science majors were taken. Choose the appropriate parameter(s) for this situation.
(A) One population proportion p.
(B) Difference between two population proportions $p_1 - p_2$
(C) One population mean $\mu_1$
(D) Difference between two population means $ \mu_11 -\mu_2$
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