Can someone please check these answers i do not think they a

Can someone please check these answers i do not think they are all right THANKS

A recent study compared the life expectancy of individuals in the UK with individuals in the US. They found that the average life expectancy in the UK was 76 and the US had an average life expectancy of 72.5. But now they want to know if the social medicine helps the variance. For a sample of 15 US individuals the sample standard deviation of life expectancy is 5. The Sample standard deviation of a sample of 13 UK citizens was 3.5. At the significance level of 0.05 can we conclude that there is a difference in the variance of the life expectancy of the two countries?

What is the null hypothesis? H0: Sigma1^2 = Sigma2^2

what is the alternative hypothesis H1: Sigma^2 is not equal to Sigma2^2

What is the appropriate test statistic f statistic...? F = 2.041

What is the critical value of the test statistic? 3.206 Or 0.328 (??)

what is your decision based on the results fail to reject null hypothesis

Interpret your results: cannot conclude that there is a difference in the variance of the life expectancy of the two countries.

Solution

What is the null hypothesis?

Let o1^2 be the variance for US individuals

Let o2^2 be the variance for UK citizens

o1^2= o2^2

What is the alternative hypothesis?

o1^2 not equal to o2^2

What is the appropriate test statistic?

F distribution

What is the calculated value of the test statistic?

F=s1^2/s2^2

=5^2/3.5^2

=2.04

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What is the critical value of the test statistic?

The degree of freedom =n1-1=15-1=14

The degree of freedom =n2-1=13-1=12

It is a two-tailed test.

Given a=0.05, the critical values of F with 0.025 and df1=14, df2=12 is 11.57 (from F table)

F with 0.975 and df1=14, df2=12 is 45.43 (from F table)

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What decision can you make based on the results?

Since F=2.04 is less than 11.57, we reject the null hypothesis.

Reject the null hypothesis