Question

A researcher analyzed whether there is a difference of microwave ovens’ price according to their performance (measured in Watts). He collected randomly prices of ovens in different shops in a city.

This researcher obtained the following results:

Groups	Size	Total	Mean	Variance
1000	8	1810	226,25	748,21
900	8	1485	185,625	2524,55
800	6	975	162,5	877,5

Sources	df	SS	MS	F	p-value
Between groups		14834,94	0,016191084
Within group	19
Total	21	42131,82

1. Test whether the average price of 900 watts and 800 watts ovens are equal by using confidence interval approach at 95%.
2. Test whether the variance of 1000 watts oven prices is equal to 750 at 5%.
3. Test at 10% whether there is a difference in the mean price of three types ovens (800, 900, 1000 Watts) by using the classical approach.
4. Determine which mean is different at 5% level.

Answer 1

1. Test whether the average price of 900 watts and 800 watts ovens are equal by using confidence interval approach at 95%.

The hypothesis being tested is:

H0: µ1 = µ2

H1: µ1 ≠ µ2

1	2
185.625	162.5	mean
50.24490024	29.62262649	std. dev.
8	6	n
	12	df
	23.125000	difference (1 - 2)
	1,838.279167	pooled variance
	42.875158	pooled std. dev.
	23.155232	standard error of difference
	0	hypothesized difference
	0.999	t
	.3377	p-value (two-tailed)

The p-value is 0.3377.

Since the p-value (0.3377) is greater than the significance level (0.05), we fail to reject the null hypothesis.

Therefore, we can conclude that the average price of 900 watts and 800 watts ovens are equal.

1. Test whether the variance of 1000 watts oven prices is equal to 750 at 5%.

The hypothesis being tested is:

H0: σ2 = 750

Ha: σ2 ≠ 750

750.0000	hypothesized variance
748.2100	observed variance of 1
8	n
7	df
6.98	chi-square
.8612	p-value (two-tailed)

The p-value is 0.8612.

Since the p-value (0.8612) is greater than the significance level (0.05), we fail to reject the null hypothesis.

Therefore, we can conclude that the variance of 1000 watts oven prices is equal to 750.

1. Test at 10% whether there is a difference in the mean price of three types ovens (800, 900, 1000 Watts) by using the classical approach.

The hypothesis being tested is:

H0: µ1 = µ2 = µ3

Ha: Not all means are equal

Sources	df	SS	MS	F	p-value
Between groups	2	14834.94	7417.47	5.162932	0.016191
Within group	19	27296.88	1436.6779
Total	21	42131.82

The p-value is 0.016191.

Since the p-value (0.016191) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that there is a difference in the mean price of three types ovens (800, 900, 1000 Watts).

1. Determine which mean is different at 5% level.

Group	Mean Difference	LSD	Significantly Different?
800-900	23.125	42.84	No
800-1000	63.75	42.84	Yes
900-1000	40.625	39.67	Yes

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