Assembly Time (Raw Data, Software Required): The makers of a child\'s swing set

Question

Assembly Time (Raw Data, Software Required):
The makers of a child's swing set claim that the average assembly time is less than 2 hours. A sample of 35 assembly times (in hours) for this swing set is given in the table below. Test their claim at the 0.10 significance level.

This is a two-tailed test.

This is a right-tailed test.

   This is a left-tailed test.

x

reject H0

fail to reject H0    

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.

(a) What type of test is this?

This is a two-tailed test.

This is a right-tailed test.

   This is a left-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.

         DATA ( n = 35 )
Assembly Time Hours    1.00 2.55 1.32 2.01 1.89 2.21 0.91 2.14 1.34 2.69 3.17 1.79 1.53 2.82 0.75 0.63 2.31 0.15 1.29 1.85 2.40 2.01 1.46 0.77 1.03 2.35 2.43 1.35 3.52 1.26 1.66 2.19 0.65 2.33 2.44

Explanation / Answer

Given that,
population mean(u)=2
sample mean, x =1.777143
standard deviation, s =0.78147
number (n)=35
null, Ho: =2
alternate, H1: <2
level of significance, = 0.1
from standard normal table,left tailed t /2 =1.307
since our test is left-tailed
reject Ho, if to < -1.307
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =1.777143-2/(0.78147/sqrt(35))
to =-1.687
| to | =1.687
critical value
the value of |t | with n-1 = 34 d.f is 1.307
we got |to| =1.687 & | t | =1.307
make decision
hence value of | to | > | t | and here we reject Ho
p-value :left tail - Ha : ( p < -1.6871 ) = 0.05037
hence value of p0.1 > 0.05037,here we reject Ho
ANSWERS
---------------
null, Ho: =2
alternate, H1: <2
test statistic: -1.687
critical value: -1.307
decision: reject Ho
p-value: 0.05037
The data supports the claim that the mean assembly time is less than 2 hours.

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