(a)
To test: The hypothesis for the significant difference between the two proportions.
(a)
Answer to Problem 27E
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.
Conclusion: Therefore, it can be concluded that the two population proportions are not equal.
(b)
To test: The relationship between the provided variables.
(b)
Answer to Problem 27E
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: There is no significant association between the being harassed online and in person.
Alternative Hypothesis: There is a significant association between being harassed online and in person.
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 and finally click on OK twice.
The desired test statistic value and p-value corresponding to one degree of freedom are obtained as
Conclusion: Therefore, there is an adequate indication at
(c)
To explain: The comparison of results obtained using chi-square test and z test.
(c)
Answer to Problem 27E
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
(d)
To explain: The reason for less number of girls reporting.
(d)
Answer to Problem 27E
Solution: The number of girls reporting harassment is low because girls are reluctant to share the details of such incidents.
Explanation of Solution
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EBK INTRODUCTION TO THE PRACTICE OF STA
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