Question

The sugar content of the syrup in canned peaches is normally distributed. Suppose that the variance is thought to be σ^2=18⁢  (milligrams)^2. A random sample of n = 10 cans yields a sample standard deviation of s = 4.8 milligrams.

(a) Test the hypothesis H0:σ^2 = 18 versus H1:σ2 ≠ 18 using α = 0.05
Find χ02 .Round your answer to two decimal places (e.g. 98.76).

Is it possible to reject H0 hypothesis at the 0.05 level of significance?

A. Yes

B. No

Find the P-value for this test.

A.	0.1<P-value<0.5

B.	0.05<P-value<0.1

C.	0.2<P-value<1

D.	0.1<P-value<0.2

(b) Suppose that the actual standard deviation is twice as large as the hypothesized value. What is the probability that this difference will be detected by the test described in part (a)?

A.

0.1

B.

0.9

C.

0.75

D.

0.25

(c) Suppose that the true variance is σ2=40. How large a sample would be required to detect this difference with probability at least 0.90?

A.

n=10

B

n=15

C

n=20

D.

n=30

Answer 1

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