Question

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Answer 1

Solution:-

SUMMARY Under 20 20 to 40 Over 40 Total Male Count Sum Average Variance 12 937 83 78.08333 70.25 20.6666751.33333 56.99242 313 78.25 292 73 332 Female Count Sum Average Variance 12 345 86.25 311 77.75 366 91.5 85.16667 83.58333 51.58333 59.66667 88.15152 Total Count Sum Average Variance 603 698 82.2575.37587.25 84.21429 37.41071 68.21429 658 ANOVA MS Source of Variation Gender Age Interaction Within P-value F crit 301.0417 568.75 16.58333 1011.25 1 301.0417 5.358467 0032632 4.413873 2 284.375 5.061805 0.018022 3.554557 2 8.291667 0.14759 0.863819 3.554557 18 56.18056 Total 1897.625 23

a) Since p-value is greater than 0.05, there is no significant interaction.

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: There is no interaction between gender and age.

Alternative hypothesis: There is interaction between gender and age.

Formulate an analysis plan. For this analysis, the significance level is 0.05.

Analyze sample data.

F statistics is given by:-

$F=\frac{MSB}{MSE}$

F = 0.148

F_critical = 3.56

The P-value = 0.86

Interpret results. Since the P-value (0.86) is greater than the significance level (0.05), we have to accept the null hypothesis.

Conclusion:-

Do not reject H₀, There is no interaction between gender and age.

b) (B) Since p-value for gender is small, rates are affected by gender.

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: u₁ = u₂

Alternative hypothesis: At-least one of the u is not equal.

Formulate an analysis plan. For this analysis, the significance level is 0.05.

Analyze sample data.

F statistics is given by:-

$F=\frac{MSB}{MSE}$

F = 5.36

F_critical = 4.41

The P-value = 0.033

Interpret results. Since the P-value (0.033) is less than the significance level (0.05), we have to reject the null hypothesis.

Conclusion:-

Reject H₀, There is sufficient evidence for significant differences between the genders.

c) (A) Since p-value for age is small, rates are affected by age.

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: u₁ = u₂ = u₃ = u₄

Alternative hypothesis: At-least one of the u is not equal.

Formulate an analysis plan. For this analysis, the significance level is 0.05.

Analyze sample data.

F statistics is given by:-

$F=\frac{MSB}{MSE}$

F = 5.06

F_critical = 3.56

The P-value = 0.018

Interpret results. Since the P-value (0.018) is less than the significance level (0.05), we have to reject the null hypothesis.

Conclusion:-

Reject H₀, There is sufficient evidence for significant differences between the age groups.