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

Claim : wish to test if the mean head circumference differs from the historical mean of 34.5 cm.

n = sample size = 15

sample mean = xbar = 34.86 cm

s = sample  standard deviation =  0.58 cm.

population mean = 34.5 cm

At the α = 0.05 significance level, test the claim

HO: µ = 34.5

HA: µ ≠ 34.5

Answer : a) this Is an  two-tail test.

Answer : b) we are testing means.

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

Answer : we reject Ho if p value is less than alpha value .

d) Find the p-value (5 points)

Answer : for this first we need to calculate test statistics value and degree of freedom

t = (x bar - population mean ) * SQRT(n) / s

t = ( 34.86 - 34.5 ) * SQRT(15) / 0.58

t = 2.403

and degree of freedom = ( n - 1 ) = 14

p value is = 0.0306 (from table)

e) you should  reject HO .

f) yes ,  the result suggest that the mean head circumference differs from 34.5 cm

now by hand written :