Question

The mean body temperature of pugs is supposed to be 102.4 F. A Vet wants to prove that the temperature is actually higher. If A sample of 64 pugs had an average temp of 103 F, with a standard deviation of .2 F, could the vet prove their claim. Use a level of significance of 0.05. What is the null hypothosis, alternative and answer?

Answer 1

Solution:

Here, we have to use one sample t test for population mean.

Null hypothesis: H₀: The mean body temperature of pugs is 102.4 F.

Alternative hypothesis: H_a: The mean body temperature of pugs is more than 102.4 F.

Null hypothesis: H₀: µ = 102.4

Alternative hypothesis: H_a: µ > 102.4

This is an upper tailed test.

We are given

Level of significance = 0.05

Xbar = 103

S = 0.2

n = 64

df = n – 1 = 63

Upper critical value = 1.6694

(by using t-table)

Test statistic formula is given as below:

t = (Xbar - µ)/[S/sqrt(n)]

t = (103 – 102.4)/[0.2/sqrt(64)]

t = 24.00

P-value = 0.00

(by using t-table)

P-value < 0.05

So, we reject the null hypothesis

There is sufficient evidence to conclude that the mean body temperature of pugs is more than 102.4 F.