Question

In: Statistics and Probability

Researchers are interested in determining if men and women’s hearts tend to be different sizes. In...

Researchers are interested in determining if men and women’s hearts tend to be different sizes. In a sample of 30 males, the mean diameter of the heart was 13.21 cm with a standard deviation of 1.05. Among 32 females, the mean diameter of the heart was found to be 11 cm with a standard deviation of 1.01. Construct a two-sided 95% confidence interval for the difference between the two means, assuming equal variance. Give an interpretation of the confidence interval.

Expert Solution

i am denoting male by 1 and female group by 2.

given data and necessary calculations are:-

the pooled estimate of standard deviation be:-

df = = ( 30+32-2) = 60

t critical value for df=60,alpha=0.05,both tailed test be:-

[ using t distribution table]

the 95% confidence interval for the difference between the two means is:-

interpretation:-

we are 95% confident that the true mean difference between men and women’s hearts sizes will be within 1.687 cm and 2.733 cm.

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orchestra answered 2 years ago

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