Question

Assembly Time (Raw Data, Software Required): The makers of a child's swing set claim that the...

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 0.01 significance level.



(a) What type of test is this?

This is a two-tailed test.

This is a left-tailed test.   

This is a right-tailed test.


(b) What is the test statistic? Round your answer to 2 decimal places.
tx =  

(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 the mean assembly time is less than 2 hours.

    

    DATA

( n = 35 )
Assembly Time

Hours   
1.12
2.57
1.39
2.12
2.05
2.34
1.03
2.24
1.35
2.83
3.25
1.86
1.55
2.86
0.86
0.71
2.36
0.24
1.39
1.96
2.46
2.06
1.59
0.87
1.08
2.49
2.49
1.54
3.57
1.40
1.78
2.26
0.68
2.42
2.55

Homework Answers

Answer #1

(a) This is a left-tailed test

(b)

Data:    

n = 35   

μ = 2   

s = 0.7772   

x-bar = 1.8663   

Hypotheses:    

Ho: μ ≥ 2   

Ha: μ < 2   

Decision Rule:    

α = 0.01   

Degrees of freedom = 35 - 1 = 34

Critical t- score = -2.44114961   

Reject Ho if t < -2.44114961   

Test Statistic:    

SE = s/√n = 0.7772/√35 = 0.131370777

t = (x-bar - μ)/SE = (1.8663 - 2)/0.131370777355001 = -1.02

p- value = 0.1580

Decision (in terms of the hypotheses):    

Since -1.017730143 > -2.44114961 we fail to reject Ho

Conclusion (in terms of the problem):    

There is not enough data to support the claim that the mean assembly time is less than 2 hours.  

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