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 *H*_{0} fail to reject
*H*_{0}

(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.

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