Question

In a sample of 40 grown-ups, the mean assembly time for a boxed swing set was 1.69 hours with a standard deviation of 0.895257 hours. The makers of this swing set claim the average assembly time is less than 2 hours.

(a) Find the test statistic.

(b) Test their claim at the 0.01 significance level.

Critical value:

Is there sufficient data to support their claim?
Yes
No

(c) Test their claim at the 0.05 significance level.

Critical value:

Is there sufficient data to support their claim?
Yes
No

Answer 1

Solution :

= 2

=1.69

=0.895257

n = 40

This is the left tailed test .

The null and alternative hypothesis is ,

H₀ :    = 2

H_a : < 2

a ) Test statistic = z

= ( - ) / / n

= (1.69-2) / 0.895257 / 40

= -2.19

Test statistic = z = -2.19

P(z <-2.19 ) =  0.0143

P-value =0.0143

b ) The critical value = -2.326

= 0.01

P-value >

0.0143 > 0.05

Fail to reject the null hypothesis .

There is not sufficient evidence to suggest that

No

c ) The critical value = -1.645

= 0.05  

P-value <

0.0143 < 0.05

Reject the null hypothesis .

There is sufficient evidence to suggest that

Yes