1. An LU professor is interested in whether there is a difference between underg
ID: 2957900 • Letter: 1
Question
1. An LU professor is interested in whether there is a difference between undergraduate students and graduate students in the amount of time spent praying each day. The professor gathers information from random samples of undergraduate and graduate students on the LU campus. The amount of time praying is normally distributed and is measured on an interval/ratio scale.
Graduate Undergraduate
15 9
17 11
10 9
13 6
11 5
17 6
a. What statistical test should be used to analyze the data?
b. Is this a one- or two tailed test?
c. Identify H0 and Ha for this study.
d. Conduct the appropriate analysis. Should H0 be rejected?
2. A teacher wants to investigate whether there is a difference between male and female students in the amount of time they spend studying for statistics. The table below shows the amount of time students spend studying statistics each week. The amounts of time spent studying are normally distributed.
Male Female
27 25
25 29
19 18
10 23
16 20
17 15
15 19
a. What statistical test should be used to analyze the data?
b. Is this a one- or two tailed test?
c. Identify H0 and Ha for this study.
d. Conduct the appropriate analysis. Should H0 be rejected?
3. A researcher is interested in whether listening to music helps or hinders test-performance. To control for differences in cognitive level, this researcher decides to use a within-participants design. He selects a random sample of participants and has them study different material of equal difficulty in both the music and no music conditions. Participants take a 20-item quiz on the material. The table below shows the scores on the quiz. The study is completely counterbalanced to control for order effects. The scores obtained are measured on an interval-ratio scale and are normally distributed.
Music No Music
17 17
16 18
15 17
16 17
18 19
18 18
a. What statistical test should be used to analyze the data?
b. Is this a one- or two tailed test?
c. Identify H0 and Ha for this study.
d. Conduct the appropriate analysis. Should H0 be rejected? What should the researcher conclude?
e. Calculate the 95 confidence interval.
Explanation / Answer
1.
a.I would recommend using a 2-sample t-test
b. It is a two-tailed test because we are just lookign for difference
Ho: There is no significant difference in the mean praying time of Undergraduates and that of Graduates
HA: There is a significant difference in the mean praying time of Undergraduates and that of Graduates
Mean of graduates=13.833; std.dev.=2.994
Mean of undergraduates=7.667; std. dev.=2.338
df=9.445
t-value=3.976
p-value=.00293; at 95% confidence, we can reject the null hypothesis and say that there is a significant difference in the mean praying time of Undergraduates and that of Graduates.
2.
a. and b. are the same as above (two-tailed, 2-sample t-test)
c. H0: Mean study time of Males and that of Females are not signficantly different
HA: Mean study time of Males and that of Females are signficantly different.
Mean study time of males: 18.429; std.dev.=5.884
Mean study time of females: 19.857; std. dev.=3.2878
df=9.415
t=-.56077
p=.588
At the 95% confidence level, we cannot reject the null hypothesis and cannot conclude that the mean study time of Males and that of Females are signficantly different.
3.
a. Matched-pairs t-test (difference of after-before
b. two-tailed (still just looking for difference)
c.Ho=The mean difference of scores on tests taken with music and scores on tests taken without music equals 0.
HA= The mean difference of scores on tests taken with music and scores on tests taken without music is significant
d. Differences (Without Music-With Music)
0
2
2
1
0
mean difference=1; std. deviation=.8944
t=2.7386
p=.04086
At the 95% confidence level, we can reject the null hypothesis and conclude that the mean difference in test scores taken with and without music is signficant. (Mean difference does not equal 0).
At the 95% confidence level, we cannot reject the null hypothesis, and cannot conclude that there is a significant difference between the mean of scores on tests taken with music and that of score on tests taken without music.
95% confidence interval: (-2.354, .3544) We are 95% confident that the true mean difference in scores is between -2.354 points and .3544 points.
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