Question

The file provided contains data on the carpace lengths, in mm, of two samples of Midland Painted Turtles (Chrysemys picta marginata). One sample is for female turtles and the other sample is for male turtles.

(i) Use the sample data to carry out a hypothesis test to test the claim that the variability of the carpace lengths is different for female Midland Painted Turtles compared to male Midland Painted Turtles. Use a significance level of 0.05.
Your answer should include:

• A statement of any assumptions required for the test.

• A comment on the strength of the evidence on which the final decision and conclusion are based

  (ii) Based on your decision and conclusion from the test in part (i), explain in one or two sentences how you would proceed if you wanted to carry out a hypothesis test to test the claim that the mean of the carpace lengths is different for female Midland Painted Turtles compared to male Midland Painted Turtles.

  (You are not required to complete this test but you must make it clear which test you would use).

Females carpace length (mm)	Males carpace length (mm)
162	120
158	102
103	117
147	112
123	93
98	120
134	103
153	96
155	117
177	104
159	135
138	119
133	128
149	116
103	94
138	127
155	131
105	101
109	106
141	121
133	107
123	125
136	113
133	114

Answer 1

	Female	Male
Mean	136.0417	113.375
Variance	451.5199	138.7663
Observations	24	24

i) Two variance test:

Significant value= 0.05

The degree of freedom:

df1= n1-1=23

df2= n2-1=23

Critical value:

The test statistic:

P-value for F test= 0.003225

The test statistic is significant and rejects null Hypothesis. There is sufficient evidence to support the claim that the variability of Female and Male is different.

ii) Based on the above problem the variance between the two samples is different.

Two sample t-test for Unequal variances:

SIgnificant value: 0.05

The degree of freedom:

The test statistic:

P-value: 0.000005

The test statistic is significant and rejects the null hypothesis. There is sufficient evidence to support the claim that the Female is different from Male.