Question

A watch manufacturer believes that 60% of men over age 50 wear watches. So, the manufacturer took a simple random sample of 275 men over age 50 and 170 of those men wore watches. Test the watch manufacturer's claim at α = .05.

a) State claim:

b) State the null and alternative hypotheses: Ho:    H1:

c) Test statistic:      (identify and round to two decimals)

d) P-value =      (rounded to four decimals)

e) Conclusion about Ho:

Answer 1

Solution :

a ) This is the right tailed test .

The null and alternative hypothesis is

H0 : p = 0.60

Ha : p >0.60

b ) n =275

x =170

= x / n = 275 / 170 = 0.62

P0 = 0.60

1 - P0 = 1 - 0.60 = 0.40

c ) Test statistic = z

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

=0.62 - 0.60 / [(0.60*0.40) / 275]

= 0.68

Test statistic = z = 0.68

d ) P(z > 0.68) = 1 - P(z < 0.68 ) = 1 - 0.7517

P-value = 0.2483

e ) = 0.05

P-value >

0.2483 > 0.05

Fail to reject the null hypothesis .

There is insufficient evidence to suggest that