Question

In a sample of 40 adults, the mean assembly time for a child's swing set was 1.75 hours with a standard deviation of 0.80 hours. The makers of the swing set claim the average assembly time is less than 2 hours. Test their claim at the 0.10 significance level.

(a) What type of test is this?

This is a left-tailed test.

This is a right-tailed test.    

This is a two-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

a)

H0: $\mu$ >= 2

Ha: $\mu$ < 2

This is left tailed test.

b)

Test statistics

t = ($\bar{x}$ - $\mu$ ) / ( S / sqrt(n) )

= (1.75 - 2) / (0.80 / sqrt(40) )

= -1.98

c)

From T table,

With test statistics 1.98 and df of 39,

p-value = 0.0274

d)

Since p-value < 0.10 level, Reject H0.

e)

The data supports the claim that the mean assembly time is less than 2 hours.