Question

The corporate CEO of "Life is Fun and Love is Strange Inc." claimed that the average sales of "Fun Life" are less than "Strange Love". In order to test the hypothesis, she asked you to conduct 2 tests. a) test the claim that the variances of the 2 stores are equal. Use a 5% significance level. b) based on your answer, use the appropriate test for the claim that the average sales of "Strange Love" are greater than "Fun Life". Use a 5% significance level for the test.

	Fun Life		Strange Love
9/2/19	$    10,499.94		$    15,602.13
9/9/19	$    12,570.94		$    15,266.79
9/16/19	$      3,005.02		$      4,081.42
9/23/19	$    14,248.23		$      1,382.24
9/30/19	$      8,636.75		$      8,275.37
10/7/19	$    14,204.85		$      1,245.25
10/14/19	$      9,543.69		$    10,673.07
10/21/19	$      5,263.17		$    10,464.89
10/28/19	$      7,371.62		$      8,938.07
11/4/19	$      5,008.26		$    10,442.26
11/11/19	$      3,489.96		$      2,108.36
11/18/19	$    12,743.37		$    13,724.84
11/25/19	$      1,848.10		$      9,319.00
12/2/19	$      5,789.95		$      7,755.35
12/9/19	$      7,586.66		$    12,327.17
12/16/19	$      2,287.95		$      2,343.91
12/23/19	$      3,356.14		$      2,444.49
12/30/19	$      4,558.28		$    12,514.89
1/6/20	$      7,247.02		$      4,998.70
1/13/20	$      7,374.31		$    13,333.44
1/20/20	$      4,593.70		$    14,156.07
1/27/20	$      1,792.20		$      6,646.60
2/3/20	$      3,248.34		$      3,494.17
2/10/20	$      1,372.53		$    17,622.30
2/17/20	$    11,061.58		$      8,109.53
2/24/20	$      9,250.06		$    11,629.81
3/2/20	$      3,598.44		$      1,294.15
3/9/20	$    13,069.25		$    14,609.46
3/16/20	$      1,769.34		$    16,544.91
3/23/20	$      5,340.35		$      6,791.68
3/30/20	$      9,584.29		$      9,749.47
4/6/20	$    14,422.19		$      3,744.22
4/13/20	$      4,139.96		$    11,331.56
4/20/20	$      4,917.33		$    10,489.14
4/27/20	$    12,172.46		$    17,745.47

Answer 1

a) test the claim that the variances of the 2 stores are equal. Use a 5% significance level.

σ₁: standard deviation of Fun Life

σ₂: standard deviation of Strange Love

Ratio: σ₁/σ₂

F method was used. This method is accurate for normal data only.

Descriptive Statistics

Variable	N	StDev	Variance	95% CI for σ²
Fun Life	35	4112.132	1.69096E+07	(1.10635E+07, 2.90276E+07)
Strange Love	35	5023.761	2.52382E+07	(1.65127E+07, 4.33246E+07)

Ratio of Variances

Estimated Ratio	95% CI for Ratio using F
0.670002	(0.338, 1.327)

Test

Null hypothesis	H₀: σ₁² / σ₂² = 1
Alternative hypothesis	H₁: σ₁² / σ₂² ≠ 1
Significance level	α = 0.05

Method	Test Statistic	DF1	DF2	P-Value
F	0.67	34	34	0.248

The p-value is 0.248.

Since the p-value (0.248) is greater than the significance level (0.05), we fail to reject the null hypothesis.

Therefore, we can conclude that the variances of the 2 stores are equal.

b) based on your answer, use the appropriate test for the claim that the average sales of "Strange Love" are greater than "Fun Life". Use a 5% significance level for the test.

The hypothesis being tested is:

H0: µ1 = µ2

H1: µ1 < µ2

Fun Life	Strange Love
7,056.1780	9,177.1480	mean
4,112.1316	5,023.7611	std. dev.
35	35	n
	68	df
	-2,120.97000	difference (Fun Life - Strange Love)
	2,10,73,901.06583	pooled variance
	4,590.63188	pooled std. dev.
	1,097.37091	standard error of difference
	0	hypothesized difference
	-1.933	t
	.0287	p-value (one-tailed, lower)

The p-value is 0.0287.

Since the p-value (0.0287) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that the average sales of "Strange Love" are greater than "Fun Life".