Question

Researchers studying infant head circumferences (in centimeters) wish to test if the mean head circumference differs from the historical mean of 34.5 cm. The researchers obtain a sample of 15 infants with a mean head circumference of 34.86 cm and a standard deviation of 0.58 cm.

At the α = 0.05 significance level, test the claim

HO: µ = 34.5

HA: µ ≠ 34.5

a) Is this an upper tail, lower tail, or two-tail test? (5 points)

b) Are we testing means or proportions? (5 points)

c) State the rule of rejection (in terms of p-value and level of significance) (5 points)

d) Find the p-value (5 points)

e) Should you reject or not reject HO? (5 points)

f) Does the result suggest that the mean head circumference differs from 34.5 cm? (5 points)

Answer 1

Here,

sample mean

sample standard deviation

and sample size

a) This is a two tail test.

b) we are testing mean.

c) The test statistic can be written as

which under H₀ follows a t distribution with n-1 df.

We reject H₀ at 0.05 level of significance if P-value < 0.05

Now,

d) The value of the test statistic =

P-value =

e) Since P-value < 0.05, so we reject H₀ at 0.05 level of significance.

f) The result suggest that the mean head circumference significantly differs from 34.5 cm.