As per records the claim of average weight of a female lion

As per records the claim of average weight of a female lion is 95.0 lbs. To check this claim, a random sample of 42 wild mountains lions (18 months or older) were captured, weighed, tagged, and released; the weights recorded in pounds yielded a sample mean of 90.0 lbs. with a standard deviation of weights is 30.7. At a 5% level of significance, does this data indicate that the true mean is less than the claim?

e. Compute p-value

f. Conclusion using critical method

g. Conclusion using p-value method

Solution

e. Compute p-value

It is a left-tailed test.

So the p-value= P(Z<-1.06) =0.1446 (from standard normal table)

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f. Conclusion using critical method

Since Z=-1.06 is larger than -1.645, we do not reject the null hypothesis.

So we can not conclude that the true mean is less than the claim

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g. Conclusion using p-value method

Since the p-value is larger than 0.05, we do not reject the null hypothesis.

So we can not conclude that the true mean is less than the claim