Question

The average weight of a package of rolled oats is supposed to be at least 16 ounces. A sample of 18 packages shows a mean of 15.81 ounces with a standard deviation of .48 ounce.

(a)	At the 5 percent level of significance, is the true mean smaller than the specification? Clearly state your hypotheses and decision rule.

a.	H0: μ ≥ 16. Reject H0 if p > 0.05
b.	H1: μ < 16. Reject H1 if p < 0.05
c.	H0: μ ≥ 16. Reject H0 if p < 0.05
d.	H1: μ < 16. Reject H1 if p > 0.05

	a
	b
	c
	d

(b)	If α = .010, we would have

a.	failed to reject the null hypothesis.
b.	rejected the null hypothesis.

	a
	b

(c)	Use Excel to find the p-value. (Round your answer to 4 decimal places.)

p-value

Answer 1

a)

H0: μ ≥ 16. Reject H0 if p < 0.05

b)

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 16
Alternative Hypothesis, Ha: μ < 16

Rejection Region
This is left tailed test, for α = 0.05 and df = 17
Critical value of t is -1.74.
Hence reject H0 if t < -1.74

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (15.81 - 16)/(0.48/sqrt(18))
t = -1.679

P-value Approach
P-value = 0.0557
As P-value >= 0.01, fail to reject null hypothesis.

c)

p value = =T.DIST(-1.679,17,TRUE)