A high school principal had just received the test scores of 100 seniors on a new mathematics achievement test.
1. A high school principal had just received the test scores of 100 seniors on a new mathematics achievement test. The mean test score for seniors was 106.78, and the mean of the achievement score for all seniors nationwide was 100 with a standard deviation of 30. The principal felt very proud. Was the principal justified? That is, did the seniors in her high school score statistically significantly higher than the mean of all students who took the test? In making this assessment, use alpha=.05
a) State the hypothesis for the test you are conducting?
b) Compute the test statistic, give the critical value, and state your decision regarding the null hypothesis using an alpha = .05
c) Calculate the effect size for your test.
d) Comment on the effect size.
e) Type a 1-3 sentence summary reporting the results as you would for a journal article.
f) Was the principal justified?
2. If the high school mentioned in the last problem had a graduating class of only 16 seniors, would this fact have changed the solutions?
a) State the hypothesis for the test your conducting.
b) Compute the test statistic, give the critical value, and state your decision regarding the null hypothesis using an alpha = .05
c) Calculate the effect size for your test. Did the effect size change from before? Why or why not?
d) Type a 1-3 sentence summary reporting the results as you would for a journal article.
e) Did the reduced sample size change the solution? Will reducing the sample size generally impact the solution and if so how?
Part II: Work the following problems using SPSS as appropriate. Be sure to attach (1) your response to all of the questions and (2) your relevant output.
3. A team of second grade teachers is uncertain about whether they are assigning an appropriate amount of homework to their students. School policy suggests that second graders have about 4 hours of homework per week. To find out if they are collectively assigning an appropriate amount of homework, they ask a random sample of the students’ parents to record the number of hours their child spends on homework over a five-week period. Does it appear that their homework assignments agree with the school’s policy? (Note: 5-week period = 20 suggested hours)
25 32 21 26 24 31 18 23 27 20 30 24 26 27 30
26 42 26 12 38 24 34 25 40 34 35 32 25 28 29
a) State the hypothesis for the test you are conducting?
b) State your decision regarding the null hypothesis using an alpha = .05. What information on the printout did you use to come to this conclusion?
c) Calculate the effect size for your test
d) Comment on the effect size.
e) Give the appropriate 95% CI and interpret the confidence interval
f) How do the values in the CI support your decision from your hypothesis test?
g) Type a 1-3 sentence summary reporting the results as you would for a journal article.
h) Does it appear that the second grade teachers are in-line with the school’s policy?
4. A study on the reaction time of children with cerebral palsy reports a mean of 1.6 seconds on a particular task. A researcher believes that the reaction time can be reduced by using a motivating set of directions. An equivalent set of children is located, and they complete the same task with the motivating set of directions. The reaction time for the twelve children follows. Does it appear that the motivating set of directions helps reduce reaction times? Use an alpha = .01.
Child A B C D E F G H I J K L
Reaction time 1.4 1.8 1.1 1.3 1.6 0.8 1.5 2.0 1.4 1.9 1.8 1.3
a) Why did the researcher sample “an equivalent set of children”?
b) State the hypothesis for the test you are conducting?
c) State your decision using an alpha= .01
d) Calculate the effect size for your test
e) Comment on the effect size.
f) Give the appropriate 99% CI and interpret the confidence interval
g) Type a 1-3 sentence summary reporting the results as you would for a journal article.
h) What might the researcher do next time to improve their chances of finding a statistically significant difference in reaction times?
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