Question

A marine biologist claims that the mean length of male harbor seals is greater than the mean length of female harbor seals. In a random sample of 89 male harbor seals the mean length is 132 centimeters and the standard deviation is 23 centimeters. In a random sample of 56 female harbor seals the mean length is 124 centimeters with a standard deviation of 18 centimeters. At ? = 0.05 can you support the marine biologist’s claim?

Create a 90% confidence interval to estimate the difference between the two mean lengths of harbor seals. (you don’t need to interpret the interval, just list it to one decimal place)

Does the confidence interval verify the results from the hypothesis test? Why?

Answer 1

The test hypothesis is

This is a one-sided test because the alternative hypothesis is formulated to detect the difference from the hypothesized mean on the upper side
Now, the value of test static can be found out by following formula:

Degrees of freedom on the t-test statistic are n1 + n2 - 2 = 89 + 56 - 2 = 143
This implies that

Since , we reject the null hypothesis H0 in favor of the alternative hypothesis .


Confidence interval(in %) = 90
z @ 90.0% = 1.6449

Required confidence interval = (132.0-124.0-5.6, 132.0-124.0+5.6)
Required confidence interval = (2.4, 13.6)

Yes confidence interval verify the result from the hypothesis test since confidence interval doesn't contain any values less than equal to 0 which tells us that the true difference of the mean will always be greater than 0 from where we can conclude that male harbor seals is greater than the mean length of female harbor seals
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