Section 1:
To test: The hypothesis for the significant difference between the two proportions.
Section 1:
Answer to Problem 40E
Solution: There is an adequate evidence to conclude that the two population proportions
Explanation of Solution
Calculation: Let
The sample proportions,
And,
Step 1: The null hypothesis
Step 2: The level of significance is denoted by
Step 3: Calculate the pooled estimate of
The pooled estimate is calculated as:
The test statistic is calculated as:
The critical values for a two-tailed test for a given level of significance can be computed form the Table A published in the book.
The value corresponding to the left tail and right tail is denoted by
Therefore,
Step 5: There is an adequate indication at 5% significance level to discard the null hypothesis. Therefore, it can be concluded that the two population proportions are not equal.
Section 2:
To test: The relationship between the two variables.
Section 2:
Answer to Problem 40E
Solution: There is an adequate indication to conclude that there is association between the two variables.
Explanation of Solution
Calculation: The hypothesis for the given problem has been defined in the following manner.
Null hypothesis: The variables ‘Being harassed online’ and ‘Being harassed in person’ are independent.
Alternative hypothesis: The variables ‘Being harassed online’ and ‘Being harassed in person’ are dependent.
The following procedure has to be followed in Minitab to obtain the test statistic value:
Step 1: Input the data of ‘Harassed in person’ and ‘Harassed online’, in column C1 and C2 respectively, in terms of ‘1’ and ‘2’, where 1 and 2 denotes ‘Yes’ and ‘No’ respectively corresponding to both the variables. Input the frequencies for both the variables in column C3.
Step 2: Go to
Step 3: Drag the variable C1 and C2 in the space provided for ‘Rows’ and ‘Columns’ respectively.
Step 4: Click on Chi-Square and select Chi-Square Test.
Step 5: Press ok two-times.
The desired test statistic value and p-value corresponding to one degree of freedom are obtained as
Therefore, there is an adequate indication at
Section 3:
To explain: The comparison of results obtained above.
Section 3:
Answer to Problem 40E
Solution: The square of the test statistic
Explanation of Solution
Therefore, it can be decided that the square of the test statistic for testing the difference of two proportions using the normal model
Section 4:
To explain: The differences in the results for boys and girls.
Section 4:
Answer to Problem 40E
Solution: The results obtained for boys are equivalent to the results obtained for the girls.
Explanation of Solution
The chi-square test conducted for testing the relationship between two variables also discarded the null hypothesis that the two categorical variables ‘Harassed online’ and ‘Harassed in person’ are independent.
Therefore, it can be concluded that there is no difference in the results obtained for both boys and girls.
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Chapter 9 Solutions
INTRO PRAC STATS LL+ SAPLING HW
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