Question

(1 point) In a sample of 40 grown-ups, the mean assembly time for a boxed swing set was 1.74 hours with a standard deviation of 0.814052 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 :

Null Hypothesis:

$H0 : \mu = 2$

Alternative Hypothesis:

$Ha : \mu < 2\; ( This\; is\; left\; tailed\; test)$

Test Statistic:

1.74 - 2 t = 0.814052 = -2.019999 V (40)

t ~ -2.02

b)

α = 0.01

df = 39,

critical value = -2.4258

calculated value of t = -2.02 is greater than critical value = -2.4258

Fail to reject null hypothesis

Option is NO

c)

α = 0.05

df = 39,

critical value = -1.6849

calculated value of t = - 2.02 is less than critical value of t = -1.6849

Reject null hypothesis

Option is Yes