Question

Assembly Time: 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 0.05 significance level.

(a) What type of test is this?

This is a right-tailed test.

This is a left-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

Solution :

Given that,

Population mean = = 2

Sample mean = = 1.75

Sample standard deviation = s = 0.80

Sample size = n = 40

Level of significance = = 0.05

a)

This is a left tailed test.

The null and alternative hypothesis is,

Ho: 2

Ha: 2

b)

The test statistics,

t = ( - )/ (s/)

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

= -1.976

c)

P-value = 0.0276

d)

Therefore, P-value = 0.0276 < = 0.05

Then it is concluded that the null hypothesis is rejected.

e)

It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the population mean μ is less than 2, at the 0.05 significance level.

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