Question

A simple random sample of 40 adult males is obtained, and the red blood cell count (in cells per microliter) is measured for each of them, with these results: n=40, bar x=4.932 million cells per microliter, s=0.504 million cells per microliter.) Use a 0.01 significance level to test the claim that the sample is from a population with a mean less than 5.4 million cells per microliter, which is often used as the upper limit of the range of normal values. Does the result suggest that each of the 40 males has a red blood cell count below 5.4 million cells per microliter? Please show step by step work

Answer 1

claim is that the sample is from a population with a mean less than 5.4 million cells per microliter

So, it is a left tailed hypothesis test

Given that

sample mean xbar = 4.932, standard deviation s = 0.504, sample size n = 40

population mean(mu) = 5.4

test statistic =

degree of freedom = n-1 = 40-1 = 39

using t table, check test statistic(-5.87) with df(39) ,we get

p value = 0.0000

it is clear that the p value is less than significance level 0.01, so we can reject the null hypothesis

Therefore, we can say that there is sufficient evidence to conclude that the mean is significantly less than 5.4