Question

Use the following information to answer Questions 22-25

The packaging of long-leaf green tea is a systematic process where the weight of each packet is tested to meet the standards. The producer of a tea company claims that the average weight of the packets is 2.20 pounds. A retailer suspects that the actual average is less than 2.20 pounds. He selects a random sample of 120 packets and obtains a mean weight of 2.18 with a standard deviation of 0.1.  

22. State the null and the alternative hypotheses.

a. H0: ? = 2.20 vs. Ha: ? ? 2.20

b. H0: ? = 2.20 vs. Ha: ? > 2.20

c. H0: ? = 2.20 vs. Ha: ? ? 2.20

d. H0: ? = 2.20 vs. Ha: ? ? 2.20

e. H0: ? = 2.20 vs. Ha: ? < 2.20

23. Which of the following is the value of the test statistic?

a. 2.19

b. –0.20

c. 0.69

d. –2.19

e. –0.69

24. Compute the observed significance of the test.

a. 0.0143

b. 0.0285

c. 0.0427

d. 0.9715

e. 0.9857

25. Determine, at the 1% level of significance, if there is sufficient evidence in the sample to reject the producer’s claim.

a. No. Since p ? ?, the decision is not to reject the producer’s claim.

b. Yes. Since p ? ?, the decision is to reject the producer’s claim.  

c. No. Since p > ?, the decision is not to reject the producer’s claim.

d. Yes. Since p > ?, the decision is to reject the producer’s claim.

e. No. Since p > ?/2, the decision is not to reject the producer’s claim.

Answer 1

22: Hypotheses are:

$H_{0}:\mu=2.20,H_{a}:\mu<2.20$

23:

Here sample size is very large so z test can be used. Following is the output of one sample z tes:

Hypothesis Test: Mean vs. Hypothesized Value
	2.2000	hypothesized value
	2.1800	mean X
	0.1000	std. dev.
	0.0091	std. error
	120	n
	-2.19	z
	.0142	p-value (one-tailed, lower)

The test statistics is -2.19.

24:

P-value = 0.0143

25:

c. No. Since p > 0.01, the decision is not to reject the producer’s claim.