# Multiple choice questions on Test of hypothesis

1) If a test of a hypothesis has a Type 1 error probability (a) of 0.01, we mean:

A) if the null hypothesis is true, we don't reject it 1% of 0.01 of the time(B) if the null hypothesis is true, we reject it 1% of the time (C) if the null hypothesis is false, we don't reject it 1% of the time (D) if the null hypothesis is false, we reject it 1% of the time.

2) A "robust" test procedure is one which:

A) requires a sophisticated level of measurement (B) requires a semi-circular shaped population (C) is sensitive to sight violations in its assumption (D) is sensitive to slight violations in its assumption

3) The operation manager at a light bulb factory wants to determine whether there is any difference in average life expectancy of bulbs manufactured on two different types of machines. The process standard deviation of Machine I is 110 hours and of Machine II is 125 hours. A random sample of 25 light bulbs obtain from Machine I indicates a sample means 375 hours ands a similar sample of 25 from Machine II indicates a sample of 362 hours. Using the 0.05 level of significance, which of the following statements offers the most accurate and appropriate measure that there is not enough evidence to conclude that there is a difference in the average life of bulbs produced by two types of machines.

+

A) Z=0.3904 and is between the critical bounds of _ 1.96 (B) t=0.0117 and is between the

+ +

critical bounds of _ 2.01 ( C ) t= 1.3829 and between the critical bounds of _2.01 (D)

+

Z=0.424 and between the critical bounds of _ 1.96

4) Which of the following would be an appropriate null hypothesis

A) The mean of population is equal to 55 (B) the mean of a sample is equal to 55 (C) the mean of a population is greater than 55 (D) only a and c are true

5) A consumer magazine sample the random arrival time for two major airline. The data on how many minute each plane was early (negative value) or late (positive values is shown below

Air Tran 5 -1 39 9 12 21 15 52 18 23

Delta 8 4 10 4 12 5 4 9 15 33 14

The correct test statistic for testing the hypothesis that there is no difference in the arrival times of planes from the two airlines is:

A) t=1.7983 (B) Z =1.2185 (C) t= 1.5240 (D) Z=2.4397

6) Are Japanese manager more motivated than American manager? A randomly selected group of each were administered the Sarnoff Survey of Attitude Toward Life (SSATL), which measure motivation for pward mobility. The score are summarized below.

American Japanese

SAMPLE SIZE 211 100

Mean SSATL Score 65.75 79.83

Population STD Dev. 11.07 6.41

Referring to the table above, suppose that the test statistic is Z= 2.45. Find the p value if we assume that the alternative hypothesis was two-tailed test(H1:A-J0).

A) 0.0071 (B) 0.0142 (C) 0.4929 (D) 0.9858

7) It is possible to directly compare the results of a confidence in interval estimate to the results obtained by testing a null hypothesis if :

A) a two tailed test for u is used (B) a one tailed test for u is used (C) both of the previous statement is true (D) none of the previous statement are true.

8) If we are performing a two-tailed test of whether u=100, the probability of detecting a shift of the mean to 105 will be ______ the probability of detecting a shift of the mean to 100.

A) less than (B) greater than (C) equal to (D) not comparable to

9) The t test for the mean difference between two related population assume that the respective

A) sample size are equal (B) sample variance are equal (C) population are approximately normal or sample size are large enough (D) all of the above

10) The use of preservative by food processors has become a controversial issue. Suppose two preservatives are extensively tested and determined safe for use in meat. A processor wants to compare the preservatives for their effects on retarding spoilage. Suppose 15 cuts of fresh meat are treated with preservatives A and 15 are treated with preservation B, and the number of hours until spoilage begin is recorded for each of the 30 cuts of meat. The results are summarized in the table below.

Preservative A Preservative B

A=106.4 hours B=96.54 hours

SA =10.3 SB =13.4 hours

Referring to the table above , which of the following is correct test statistic for determining if the population variance differ for preservation A and B?

A) F=-3.10 (B) F=0.5908(C) F=0.7687 (D) F=0.8250

11) In testing for the differences between the means of 2 independent population where the variances in each population are unknown but assumed equal, the degree of freedom are:

A) n-1 (B) n1+ n2-1 (C) n1+n2-2. (D) n-2

#### Solution Preview

Please see attached file for answers.

1) If a test of a hypothesis has a Type 1 error probability (a) of 0.01, we mean:

A) if the null hypothesis is true, we don't reject it 1% of 0.01 of the time (B) if the null hypothesis is true, we reject it 1% of the time (C) if the null hypothesis is false, we don't reject it 1% of the time (D) if the null hypothesis is false, we reject it 1% of the time.

Answer: (B) if the null hypothesis is true, we reject it 1% of the time

2) A "robust" test procedure is one which:

A) requires a sophisticated level of measurement (B) requires a semi-circular shaped population (C) is sensitive to sight violations in its assumption (D) is sensitive to slight violations in its assumption

Note: Please check your answer choices. The correct answer choice has not been provided as any of the 4 alternatives

Robust testing procedures are hypothesis testing techniques that are relatively insensitive to violations of assumptions such as normality and homoscedasticity.

3) The operation manager at a light bulb factory wants to determine whether there is any difference in average life expectancy of bulbs manufactured on two different types of machines. The process standard deviation of Machine I is 110 hours and of Machine II is 125 hours. A random sample of 25 light bulbs obtain from Machine I indicates a sample means 375 hours ands a similar sample of 25 from Machine II indicates a sample of 362 hours. Using the 0.05 level of significance, which of the following statements offers the most accurate and appropriate measure that there is not enough evidence to conclude that there is a difference in the average life of bulbs produced by two types of machines.

+

A) Z=0.3904 and is between the critical bounds of _ 1.96 (B) t=0.0117 and is between the

+ +

critical bounds of _ 2.01 ( C ) t= 1.3829 and between the critical bounds of _2.01 (D)

+

Z=0.424 and between the critical bounds of _ 1.96

Answer: A) Z=0.3904 and is between the critical bounds of +/- 1.96

Note : This is a test where small sample sizes (<30) are involved and hence the appropriate test is t test

But the answer choice , t= 0.3904 and is between the critical bounds of +/- 2.01 is not available

The next best choice is A) Z=0.3904 and is between the critical bounds of +/- 1.96

Difference between means (large sample size)

At significance ...

#### Solution Summary

Multiple choice questions on hypothesis testing-related with Type 1 error probability, rejecting/ accepting Null Hypothesis, t statistic , p-value, mean difference between two related population , two tailed test, F statistic, degree of freedom etc are answered.