A simple random sample of 53 adults is obtained from a normally distributed popu

Question

A simple random sample of 53 adults is obtained from a normally distributed population, and each person's red blood cell count (in cells per microliter) is measured. The sample mean is 5.29 and the sample standard deviation is0.55.
Use a 0.05 significance level and the given calculator display to test the claim that the sample is from a population with a mean less than 5.4,
which is a value often used for the upper limit of the range of normal values. What do the results suggest about the sample group? A simple random sample of 53 adults is obtained from a normally distributed population, and each person's red blood cell count (in cells per microliter) is measured. The sample mean is 5.29 and the sample standard deviation is0.55.
Use a 0.05 significance level and the given calculator display to test the claim that the sample is from a population with a mean less than 5.4,
which is a value often used for the upper limit of the range of normal values. What do the results suggest about the sample group?

Explanation / Answer

Sample size, n = 50
Hypotheses:
Null: Ho: = 5.4
Alternative : Ha : < 5.4 (CLAIM)
Test to be used: Left-tailed z-test
Test statistic: z-score = [x-bar – ] / s)
= [5.29–5.4] / (0.55)
= -0.2

P-value = P(z -0.2) = 0.4207

As the value is less than 0.05, it is not in rejection region

AS THE STATISTIC DOES NOT LIE IN THE REJECTION REGION, WE ACCEPT THE NULL HYPOTHESIS

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