Some measurements in mm were made on a species of spider named Sosippus Floridan

Question

Some measurements in mm were made on a species of spider named Sosippus Floridanus that are native to Florida. There are 10 female spiders and 10 male spiders. The total body lengths are as follows:

Female 11.06 13.87 12.93 15.08 17.82 14.14 12.26 17.82 20.17 16.88

Male 12.26 11.66 12.53 13.00 11.79 12.46 10.65 10.39 12.26 14.07

a. Compute a confidence interval, a = .05, for the ratio of the variance of body sizes in female and male spiders. b. Test the null hypothesis that the variance of the lengths of female and male spiders are equal against the alternative that they are different

Explanation / Answer

Some measurements in mm were made on a species of spider named Sosippus Floridanus that are native to Florida. There are 10 female spiders and 10 male spiders.

Here we have to find 95% confidence interval for the ratio of the variance of body sizes in female and male spiders.

And also we have to test the hypothesis that,

H0: Variances are equal.

H1 : Variances are not equal.

BOth the questions we can done using MINITAB.

steps :

ENter all the data in MINITAB sheet --> Stat --> Basic statistics --> 2-Variances --> Samples in different columns --> First : select first data column --> second : select second data column --> options : 95.0 --> ok --> Storage : select all the options --> ok --> ok

Test for Equal Variances for female, male

Test for Equal Variances: female, male

95% Bonferroni confidence intervals for standard deviations

N Lower StDev Upper
female 10 1.88949 2.88858 5.81660
male 10 0.70223 1.07354 2.16174

F-Test (normal distribution)
Test statistic = 7.24, p-value = 0.007

Levene's Test (any continuous distribution)
Test statistic = 8.10, p-value = 0.011

Test statistic F = 7.24

P-value = 0.007

P-value < alpha

Reject H0 at 5% level of significance.

Conslusion : Two variances are not equal.

95% confidence interval for female is (1.88494, 5.81660).

95% confidence interval for male is (0.70223, 2.16174).

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