Question

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Q3:

A sample of 100 body temperatures has a mean of 98.8℉. Assume that ? is known to be 0.6℉. Use a 0.05 significance level to test the claim that the mean body temperature of the population is equal to 98.6℉, as is commonly believed. Is there sufficient evidence to conclude that the common belief is wrong?

(Use the P-value method where (? < 3.33) = 0.9996)

Q4:

Listed below are the body lengths (in inches) and weights (in lb) of randomly selected bears:

Length

40      64        65        49        47

Weight

65      356      316      94        86

            •           Find the value of the linear correlation coefficient.

            •           Letting y represent weights of bears and letting x represent their lengths, find the regression equation.

            •           Based on the given sample data, what is the best predicted weight of a bear with a length of 72.0 inch?

Answer 1

Question 3)

Answer)

As the population standard deviation is known here, we can use standard normal z table to conduct the test.

Null hypothesis Ho : u = 98.6

Alternate hypothesis Ha : u is not equal to 98.6

This is a two tailed test.

As not equal to sign in alternate hypothesis means two tailed test.

Test statistics z = (sample mean - claimed mean)/(s.d/√n)

Sample mean = 98.8

Claimed mean = 98.6

Sample size N = 100

After substitution z = 3.33

From z table, P(z>3.33) = 0.0004

But our test is two tailed

So, P-Value is = 0.0004*2 = 0.0008

As the obtained P-Value is less than the given alpha of 0.05

We reject the null hypothesis and we do not have enough evidence to support the claim.