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 0.01 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

Answer 1

: Hypothesized population mean = 2

claim :  the average assembly time is less than 2 hours

Null hypothesis : H_o : average assembly time = 2 ;

Alternate hypothesis : H_a : average assembly time < 2 ;

(a) What type of test is this?

Left tailed test (Alternate hypothesis has < )

(b)

n: sample size = 35

Sample mean : Sample average assembly time :

Sample standard deviation :

	Hours	x-xbar	x-xbar2
	1.12	-0.7463	0.5570
	2.57	0.7037	0.4952
	1.39	-0.4763	0.2269
	2.12	0.2537	0.0644
	2.05	0.1837	0.0337
	2.34	0.4737	0.2244
	1.03	-0.8363	0.6994
	2.24	0.3737	0.1397
	1.35	-0.5163	0.2666
	2.83	0.9637	0.9287
	3.25	1.3837	1.9146
	1.86	-0.0063	0.0000
	1.55	-0.3163	0.1000
	2.86	0.9937	0.9874
	0.86	-1.0063	1.0126
	0.71	-1.1563	1.3370
	2.36	0.4937	0.2437
	0.24	-1.6263	2.6449
	1.39	-0.4763	0.2269
	1.96	0.0937	0.0088
	2.46	0.5937	0.3525
	2.06	0.1937	0.0375
	1.59	-0.2763	0.0763
	0.87	-0.9963	0.9926
	1.08	-0.7863	0.6183
	2.49	0.6237	0.3890
	2.49	0.6237	0.3890
	1.54	-0.3263	0.1065
	3.57	1.7037	2.9026
	1.4	-0.4663	0.2174
	1.78	-0.0863	0.0074
	2.26	0.3937	0.1550
	0.68	-1.1863	1.4073
	2.42	0.5537	0.3066
	2.55	0.6837	0.4674
Total	65.32		20.5374
Mean: 65.32/35=	1.8663

Test Statistic : t = -1.0175

(c)

Degrees of freedom = n-1 = 35-1 = 34

significance level: = 0.05

For left tailed test :

p-value = 0.1581

(d)

As P-Value i.e. is greater than Level of significance i.e (P-value:0.1581 > 0.01:Level of significance); Fail to Reject Null Hypothesis

conclusion regarding the null hypothesis

Ans : fail to reject H₀

(e) Choose the appropriate concluding statement.

Ans : We reject the claim that the mean assembly time is less than 2 hours.

For finding p-value; Excel function T.DIST.RT is being used

T.DIST.RT function
Returns the right-tailed Student's t-distribution.
The t-distribution is used in the hypothesis testing of small sample data sets. Use this function in place of a table of critical values for the t-distribution.
Syntax
T.DIST.RT(x,deg_freedom)
The T.DIST.RT function syntax has the following arguments:
• X Required. The numeric value at which to evaluate the distribution.
• Deg_freedom Required. An integer indicating the number of degrees of freedom.