A marketing consultant was in the process of studying the perceptions of married couples concerning their weekly food expenditures. He believed that the husband's perception would be higher than the wife's. To judge his belief, he takes a random sample of ten married couples and asks each spouse to estimate the family food expenditure (in dollars) during the previous week. If the test statistic t = 2.776, with a degrees of freedom = 9, what can we conclude at α =.05?

Question

Lea Cunningham

Mathematics

14 October, 18:43

A marketing consultant was in the process of studying the perceptions of married couples concerning their weekly food expenditures. He believed that the husband's perception would be higher than the wife's. To judge his belief, he takes a random sample of ten married couples and asks each spouse to estimate the family food expenditure (in dollars) during the previous week. If the test statistic t = 2.776, with a degrees of freedom = 9, what can we conclude at α =.05?

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Alina Rice · Answer 1

We have sufficient evidence to conclude at α =.05 that the husband's perception would be higher than the wife's.

Step-by-step explanation:

The hypotheses testing procedure in the given scenario is

H0: Husband's perception would be similar to the wife's i. e. μh=μw

Ha: Husband's perception would be higher than the wife's i. e. μh>μw

Level of significance: α=0.05

Test statistic: t=2.776

Critical region: t>t (0.05,9) = 1.833

Conclusion: As the calculated value of t lies in critical region, so we reject our null hypothesis at 0.05 level of significance. Thus, we have sufficient evidence to conclude at α =.05 that the husband's perception would be higher than the wife's.