A researcher believed that there was a difference in the amount of time boys and girls | Solution

1.      A researcher believed that there was a difference in the amount of time boys and girls at 7th grade studied by using a two-tailed t test. Which of the following is the null hypothesis?

a.Mean of hours that boys studied per day was equal to mean of hours that girls studied per day

b. Mean of hours that boys studied per day was greater than mean of hours that girls studied per day

c. Mean of hours that boys studied per day was smaller than mean of hours that girls studied per day

d. Mean of hours that boys studied per day was smaller than or equal to mean of hours that girls studied per day

2.      A professor assumed there was a correlation between the amount of hours people were expose to sunlight and their blood vitamin D level. The null hypothesis was that the population correlation was__

a. Positive 1.0

b. Negative 1.0

c. Zero

d. Positive 0.50

3.      Conventionally, the null hypothesis is false if the probability value is:

a. Greater than 0.05

b. Less than 0.05

c. Greater than 0.95

d. Less than 0.95

4.      A teacher hypothesized that in her class, grades of girls on a chemistry test were the same as grades of boys. If the probability value of her null hypothesis was 0.56, it suggested:

a. We failed to reject the null hypothesis

b. Boys’ grades were higher than girls’ grades

c. Girls’ grades were higher than boys’ grades

d. The null hypothesis was rejected

5.      Which of the following could reduce the rate of Type I error?

a. Making the significant level from 0.01 to 0.05

b. Making the significant level from 0.05 to 0.01

c. Increase the β level

d. Increase the power

6.      ___is the probability of a Type II error; and ___ is the probability of correctly rejecting a false null hypothesis.

a. 1-β; β

b. β; 1-β

c. α; β

d. β; α

7.      A student hypothesized that girls in his class had the same blood pressure levels as boys. The probability value for his null hypothesis was 0.15. So he concluded that the blood pressures of the girls were higher than boys’. Which kind of mistake did he make?

a. Type I error

b. Type II error

c. Type I and Type II error

d. He did not make any mistake

8.      When you conduct a hypothesis testing, at which of the following P-value, you feel more confident to reject the null hypothesis?

a. 0.05

b. 0.01

c. 0.95

d. 0.03

9.      A student posed a null hypothesis that during the month of September, the mean daily temperature of Boston was the same as the mean daily temperature of New York. His alternative hypothesis was that mean temperatures in these two cities were different. He found the P value of his null hypothesis was 0.56. Thus, he could conclude:

a. In September, Boston was colder than New York

b. In September, Boston was warmer than New York

c. He may reject the null hypothesis

d. He failed to reject the null hypothesis

10.  If the P-value of a hypothesis test is 0.40, you conclude

a. You accept the null hypothesis

b. You reject the null hypothesis

c. You failed to reject the null hypothesis

d. You think there is a significant difference

11.  Imagine that a researcher wanted to know the average weight of 5th grade boys in a high school. He randomly sampled 5 boys from that high school. Their weights were: 120 lbs., 99 lbs, 101 lbs, 87 lbs, 140 lbs. What’s the sample standard deviation (show work)?

12.  Imagine that a researcher wanted to know the average weight of 5th grade boys in a high school. He randomly sampled 5 boys from that high school. Their weights were: 120 lbs., 99 lbs, 101 lbs, 87 lbs, 140 lbs. What’s the standard error of the mean (show work)?

13.  Imagine that a researcher wanted to know the average weight of 5th grade boys in a high school. He randomly sampled 5 boys from that high school. Their weights were: 120 lbs., 99 lbs, 101 lbs, 87 lbs, 140 lbs. The researcher posed a null hypothesis that the average weight for boys in that high school should be 100 lbs. What is the absolute value of calculated t that we use for testing the null hypothesis (Show work)?

14.  Imagine a researcher posed a null hypothesis that in a certain community, the average energy expenditure should be 2,100 calories per day. He randomly sampled 100 people in that community. After he computed the t value by calculating a two-tailed t-statistic, he found that the probability value was 0.10. Thus, he concluded:

a. The average energy expenditure was bigger than 2,100 calories per day

b. The average energy expenditure was smaller than 2,100 calories per day

c. He could not reject the null hypothesis that the average energy expenditure was 2,100 calories per day

d. The average energy expenditure was either more than 2,100 calories per day or less than 2,100 calories per day

15.  Compared to the normal distribution, the t distribution has ___ values at the top and ___ at the tails.

a. More; less

b. More; more

c. Less; less

d. Less; more

16.  In order to test if there is a difference between means from two populations, which of following assumptions are NOT required?

a. The dependent variable scores must be a continuous quantitative variable.

b. The scores in the populations are normally distributed.

c. Each value is sampled independently from each other value.

d. The two populations have similar means

17.  A researcher posed a null hypothesis that there was no significant difference between boys and girls on a standard memory test. He randomly sampled 100 girls and 120 boys in a community and gave them the standard memory test. The mean score for girls was 70 and the standard deviation of mean was 5.0. The mean score for boys was 65 and the standard deviation of mean was 6.0. What’s the absolute value of the difference between means (Show work)?

18.  A researcher posed a null hypothesis that there was no significant difference between boys and girls on a standard memory test. He randomly sampled 100 girls and 100 boys in a community and gave them the standard memory test. The mean score for girls was 70 and the standard deviation of mean was 5.0. The mean score for boys was 65 and the standard deviation of mean was 5.0. What is the standard error of the difference in means (Show work)?

19.  A researcher posed a null hypothesis that there was no significant difference between boys and girls on a standard memory test. He randomly sampled 100 girls and 100 boys in a community and gave them the standard memory test. The mean score for girls was 70 and the standard deviation of mean was 5.0. The mean score for boys was 65 and the standard deviation of mean was 5.0. What’s the t-value (two-tailed) for the null hypothesis that boys and girls have the same test scores (Show work)??

20.  Which of the following involves making pairwise comparisons?

a. Comparing the standard deviation of GRE grades between two states

b. Comparing the variance of the amount of soda consumed by boys and girls in a high school

c. Comparing the mean weight between children in grades 2, 3, 4 and 5

d. Comparing the number of restaurants in New York and Boston