10.33 According to a study conducted by a major computer company, 59% of men and

Question

10.33 According to a study conducted by a major computer company, 59% of men and 70% of women say that weight is an extermely/very important factor in purchasing a laptop computer. Suppose this survey was conducted using 374 men and 481 women. Do these data show enough evidence to declare that a significantly higher proportion of women than men believe that weight is an extremely/very important factor in purchasing a laptop computer? Use a 5% level of significance.

a) write down null and alternative statement

b) write down conclusions using 3 approaches (Critical Value approach, Ztest and P value approach)

c) write down implication

d) write down validity

(Please show me step by step calculations)

Explanation / Answer

Solution :

Male Data

n1= 374

p1 = 0.59

Female Data

n2= 481

p2 = 0.70

Ho ; p1 - p2 = 0

Ha : p1 - p2 0

we use two-tailed test.

Note that sample size is large, so z-test can be done instead of t-test as t-test coincides with z-test for large sample ,

p = (0.59*374+0.7*481)/(374+481) = 0.65

z = (p1 - p2) - (p1 - p2)_hypothesized /sqrt(p(1-p)*(1/n1 + 1/n2 ))

= – 3.34

Now p-value = P(z<–3.34) + P(z>3.34) = 0.001 (approx)

Decision: As p-value is less than level of significance = 0.05

We are to reject the null hypothesis Ho ; p1 - p2 = 0 under level of significance = 0.05

Conclusion: These data do not show enough evidence to support the conclusion that there is no difference in the proportion of men and women who think weight is a factor in purchasing a laptop.

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