A study tested 559 high school students using a leisure-interest checklist (LIC)
ID: 3229247 • Letter: A
Question
A study tested 559 high school students using a leisure-interest checklist (LIC) survey. The means and standard deviations for each of the sevel LIC factor scales are given in the following table for n=252 male students and n=307 female students.'
a) Without looking at the data, would you expect that boys would have a greater or lesser interest in sports as a leisure time activity? Based on your conjecture, what alternative hypothesis would you choose to test versus the null hypothesis that there is no difference in the mean LIC scores for boys and girls?
b) Does the alternative hypothesis you posed in (a) correspond to a one-tailed or a two-tailed statistical test?
Please write clearly thanks!
LIC factor Males Males Females Females scale activity mean s mean s hobbies 10.06 6.47 13.64 7.46 social fun 22.05 5.12 25.96 5.07 sports 13.65 4.82 9.88 4.41 cultural 11.48 5.69 13.21 5.31 trips 6.90 3.41 6.49 2.97 games 4.95 3.29 3.85 2.49 church 2.15 2.10 3.00 2.26 a 0.01Explanation / Answer
(a) Yes, without looking at the data, i expect that boys would have a greater interest in sports as a leisure time activity.
Alternative Hypothesis : Ha : Boys have greater interest in sports as a leisure time than girls as a lieasure activity. boys > girls
(b) The alternative hypothesis posed a one tailed hypothesis statstical test.
(c) Test statisitc
Pooled standard deviation sp =sqrt [(nb -1)sb2 + (ng -1)sg2]/ (nb +ng -2] =sqrt [(251 * 4.822 + 306 * 4.412 )/557] = 4.60
Standard error of sampling se0 = sp * sqrt [1/nb +1/ng ] = 4.60 *sqrt [ 1/252 + 1/307] = 0.3982
so Test Statistic
t = (boys - girls)/ se0 = (13.65 - 9.88)/ 0.3982 = 9.47
so tcritical = 2.33 for alpha = 0.01
so here t > tcritical so we can reject the null hypotheiss and can conclude that Boys have greater interest in sports as a leisure time than girls as a lieasure activity.
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