Question

The marketing manager for an automobile manufacturer is interested in determining the proportion of new compact-car owners who would have purchased a passenger-side inflatable air bags if it had been available for an additional. The manager believes that (from historical data) that the proportion of customers want side air bags is different from 30%. Suppose that a survey of 200 new compact-car owners is selected and 79 indicate that they would have purchased the air bags. At α = 0.10 level of significance, is there enough evidence to claim that the population proportion will be different from 30%?

(a) Hypothesis: H0 :

Ha :

(b) Test Statistics=

(c) Pvalue=

(d) Decision:

(e) Conclusion:

Answer 1

Solution :

a ) This is the two tailed test .

The null and alternative hypothesis is

H0 : p = 0.30

Ha : p 0.30

n = 200

x = 79

= x / n = 79 / 200 = 0.39

P0 = 0.30

1 - P0 = 1-0.30 = 0.70

b )Test statistic = z

= - P0 / [P0 * (1 - P0 ) / n]

= 0.39 - 0.30 / [(0.30*0.70) / 200 ]

= 2.78

Test statistic = z = 2.78

c ) P(z > 2.78 ) = 1 - P(z < 2.78) = 1 - 0.9973

P-value = 2 * 0.0027 =0.0054

= 0.10

P-value <

0.0054 < 0.10

d ) Reject the null hypothesis .

e ) There is sufficient evidence to suggest that