Question

21)____________     A washing machine manufacturer says that 85% of its washers last five years        

                                  before repairs are necessary. A random sample of 100 washers showed that 79 of

22)____________     them lasted five years before they needed repair. Test to see if there is a        

                                  difference between the manufacturer claim and the sample results. List the

23)____________     21) test statistic     22) p-value     23) Does this data indicate that the

                                  manufacturer’s claim is too high or too low? (yes or no)        

Answer 1

H0: p = 0.85 , Ha: p 0.85

Sample proportion = 79 / 100 = 0.79

Test statistics

z = ( - p) / sqrt [ p ( 1 - p) / n ]

= ( 0.79 - 0.85) / sqrt [ 0.85 * ( 1 - 0.85) / 100 ]

= -1.68

p-value = 2 * P(Z < z)

= 2 * P(Z < -1.68)

= 2 * 0.0465

= 0.0930

since p-value > 0.05 , fail to rejetc H0.

No, we do not have sufficient evidence to support the claim.