Question

Assembly Time: In a sample of 40 adults, the mean assembly time for a child's swing set was 1.77 hours with a standard deviation of 0.76 hours. The makers of the swing set claim the average assembly time is less than 2 hours. Test their claim at the 0.01 significance level.

(a) What type of test is this?

This is a left-tailed test. This is a two-tailed test.     This is a right-tailed test.

(b) What is the test statistic? Round your answer to 2 decimal places.
t

_x

=

(c) Use software to get the P-value of the test statistic. Round to 4 decimal places.
P-value =

(d) What is the conclusion regarding the null hypothesis?

reject H₀ fail to reject H₀    

(e) Choose the appropriate concluding statement.

The data supports the claim that the mean assembly time is less than 2 hours. There is not enough data to support the claim that the mean assembly time is less than 2 hours.      We reject the claim that the mean assembly time is less than 2 hours. We have proven that that the mean assembly time is less than 2 hours.

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis: μ = 2
Alternative Hypothesis: μ < 2

Rejection Region

a)

This is left tailed test, for α = 0.01 and df = 39

Critical value of t is -2.426.
Hence reject H0 if t < -2.426

b)

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (1.77 - 2)/(0.76/sqrt(40))
t = -1.91

c)

P-value Approach
P-value = 0.0315

d)

As P-value >= 0.01, fail to reject null hypothesis.

e)

There is not enough data to support the claim that the mean assembly time is less than 2 hours.