Question 2 A study measuring fitness level in teens randomly sampled 112 male te

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Question 2

A study measuring fitness level in teens randomly sampled 112 male teens and 101 female teens with a higher score indicating more fitness. Researchers suspected that the fitness level for male teens (1) is higher than for female teens (2), and wanted to check whether the data would supported this hypothesis.

The following hypotheses were tested:

H0: µ1 = µ2

Ha: µ1 > µ2

t-test of difference: df = 210 t-value = 0.25 p-value = 0.400

Which of the following is an appropriate conclusion based on the output?

A. The data provide sufficient evidence to conclude that male and female teens do not differ in mean fitness score.

B. The data do not provide sufficient evidence to reject H0, so we accept it, and conclude that female and male teens do not differ in mean fitness score.

C. The data do not provide sufficient evidence to conclude that the mean fitness score of male teens is higher than that of female teens.

D.The data provide sufficient evidence to reject H0 and to conclude that the mean fitness score for male teens is higher than that of female teens.

Question 3

As first year residential students get familiar with campus life, some students spend less time speaking with the residential advisor. Suppose individual call time (in minutes) is measured in September and then later in December. The results are as shown:

We wish to test whether there is a statistically significant decrease in individual call time.

Given the design of the study and the question of interest, which one of the following statistics test is relevant to use?

A. Paired t-test and CI: Sept; Dec

B. Two-sample t-test and CI: Sept; Dec

Question 4

Using four methods to teach ANOVA, do these four samples differ enough from each other to reject the null hypothesis that type of instruction has no effect on mean test performance?

Since we are comparing more than 2 groups, we will use ANOVA to test whether the data provide evidence that test score is related to teaching method.

One of the conditions that allows us to use ANOVA safely is that of equal (population) standard deviations. Can we assume that this condition is met in this case?

Yes, since 0.793 0.360 < 2.

No, since 0.793/0.360 > 2

No, since the four sample standard deviations are not all equal.

No, since the population standard deviations are not given, so we cannot check this condition.

Question 5

Using four methods to teach ANOVA, do these four samples differ enough from each other to reject the null hypothesis that type of instruction has no effect on mean test performance?

Since we are comparing more than 2 groups, we will use ANOVA to test whether the data provide evidence that SAT score is related to study strategy.

The following hypotheses were tested:

H0: µ1 = µ2 = µ3= µ4

Ha: µ1, µ2, µ3, µ4 are not all equal

The analysis was run on the data and the following output was obtained:

Which of the following is a valid conclusion based on this output?

A. The data provide strong evidence that the four mean scores (representing the four teaching strategies) are not all equal.

B.The data do not provide sufficient evidence that scores are related to teaching strategy.

Question 6

A researcher wanted to determine if teaching approaches influence second graders’ ability to do columnar addition. To test this, the researcher randomly selected 75 second graders from a local school and assigned them to one of three teaching conditions: (1) rote memory, (2) manipulatives, or (3) computer. One group of 25 students were taught using rote memory, a second group of 25 students was taught using manipulatives, and a third group of 25 students was taught with a calculator. All students were given a test on columnar addition. The means and standard deviations for the three groups are shown below.

Mean Number of Correct Answers for Three Groups of Second Grade Students on a Test of Columnar Addition

What hypothesis testing technique should the researcher use to analyze the data?

A. Paired t-test

B. z-test for the population mean

C. ANOVA

D. Two-sample t-test

Question 7

Do TV viewers differ, on average, in terms of the amount of television that they watch during the month of January as opposed to June? A researcher conducted a hypothetical study, where the she randomly selected 50 TV viewers and recorded the number of minutes of television watched during January and then again in July. The researcher wanted to determine whether there is a difference in mean number of minutes of television viewing in January and in July.

What hypothesis testing technique should the researcher use to analyze the data?

A. ANOVA

B. z-test for the population mean

C. Paired t-test

D. Two-sample t-test

Sample N Mean SD 1(M) 112 7.38 6.95 2(F) 102 7.15 6.31

Explanation / Answer

Solution:

Question 2) Which of the following is an appropriate conclusion based on the output?

P-value>0.05. So, the given statement.

A. The data provide sufficient evidence to conclude that male and female teens do not differ in mean fitness score.

Question 3) A. Paired t-test and CI: Sept; Dec

Because from the data we can say that the data not indepedent.

Question 4)  No, since 0.793/0.360 > 2

Question 5) P-value<0.001

A. The data provide strong evidence that the four mean scores (representing the four teaching strategies) are not all equal.

Question 6) C. ANOVA

Because there are three groups in the table.

Question 7) The researcher wanted to determine whether there is a difference in mean number of minutes of television viewing in January and in July.

So, C. Paired t-test

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