Question

# Assembly Time: In a sample of 40 adults, the mean assembly time for a child's swing...

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.

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.

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