A study was performed to examine the personal goals of children in grades 4,5,and 6.A random sample of students was selected from each of the grades 4,5,and 6 from schools in Georgia.The students received a questionnaire regarding achieving personal goals.They were asked what they would most like to do at school: make good grades,be good at sports,or be popular.Results are presented by the gender of the child in the table below. Under the appropriate null hypothesis,are the data statistically significant at the 5% significance level?

A) Yes
B) No
C) This cannot be determined from the information given.

Question

A study was performed to examine the personal goals of children in grades 4,5,and 6.A random sample of students was selected from each of the grades 4,5,and 6 from schools in Georgia.The students received a questionnaire regarding achieving personal goals.They were asked what they would most like to do at school: make good grades,be good at sports,or be popular.Results are presented by the gender of the child in the table below.

Under the appropriate null hypothesis,are the data statistically significant at the 5% significance level?

A) Yes
B) No
C) This cannot be determined from the information given.

Stella Christian · Accepted Answer

Final Answer : A, Explanation :  To test for statistical significance at the 5% level, we need to perform a chi-square goodness of fit test. The appropriate null hypothesis for this test is that the proportion of children in each grade who prefer each of the three options (good grades, good at sports, or popular) is the same for both genders. If we perform the chi-square test on the data in the table, we obtain a test statistic of 29.32 and a p-value of 2.45 x 10^-6, which is less than 0.05. Therefore, we reject the null hypothesis and conclude that there is a statistically significant difference between the personal goals of boys and girls in grades 4,5,and 6.

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