Question

In the following part, assume that, even if the sample is not normally distributed, the population is.

2) In the last 36 weeks, Fun life's manager implemented a customer service policy to reduce the variation in sales among her customer. Test the claim that the variance is less than the old value of 4355. Use a 7% significance level

	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

using excel>Addin>phstat>one sample test

we have

Chi-Square Test of Variance
Data
Null Hypothesis                        s^2=	4355
Level of Significance	0.07
Sample Size	35
Sample Standard Deviation	4528.178
Intermediate Calculations
Degrees of Freedom	34
Half Area	0.035
Chi-Square Statistic	160080.2443
Lower-Tail Test
Lower Critical Value	22.70930061
p-Value	1
Do not reject the null hypothesis

since p value is greater than 0.07 so we do not reject Ho and conclude that  the variance is not less than the old value of 4355