Question

The mean birth weight of infants in the United
States is μ = 3315 grams. Let X be the birth weight
(in grams) of a randomly selected infant in Jerusalem.
Assume that the distribution of X is N(μ, σ2), where μ
and σ2 are unknown.We shall test the null hypothesis H0:
μ = 3315 against the alternative hypothesisH1:μ < 3315,
using n = 30 randomly selected Jerusalem infants.
(a) Define a critical region that has a significance level of
α = 0.05.
(b) If the random sample of n = 30 yielded x = 3189 and
s = 488, what would be your conclusion?
(c) What is the approximate p-value of your test?

Answer 1

a)

df = n -1 = 30 - 1 = 29

t critical value at 0.05 significance level with 29 df = -1.699

Critical region = Reject H0 if test statistics t < -1.699

b)

Test statistics

t = - / (S / sqrt(n) )

= 3189 - 3315 / (488 / sqrt(30) )

= -1.41

Since test statistics falls in non-rejection region , we do not have sufficient evidence to reject H0.

We conclude at 0.05 level that we fail to support the claim.

c)

From T table,

With test statistics 1.41 and df of 29 , p-value lie between 0.05 < p < 0.10

p-value = 0.0846