Question

1. A 95% CI for a population mean is 44.1±4.88

.(a) Can you reject the null hypothesis that ?=37 at the 5% level? (Type: YES or NO or CANNOT TELL):

(b) Can you reject the null hypothesis that ?=48 at the 5% level? (Type: YES or NO or CANNOT TELL):

(c) In general, you fail to reject the null hypothesis if ? is the confidence interval. (Type: IN or NOT IN) :

2 . A random sample of size ? has been selected from a normally distributed population whose standard deviation is ?. In hypothesis testing for the population mean, the t-test should be used instead of the z-test if:
A. ?>30 and ? is unknown
B. ?<30 and ? is known
C. both A and B are true
D. both A and B are false

In selecting the sample size to estimate the population proportion ?

, if we have no knowledge of even the approximate value of the sample proportion ?̂ , we:
A. let ?̂ =0.50
B. take another sample and estimate ?̂
C. let ?̂ =0.95
D. take two more samples and find the average of their ?̂

Answer 1

1.

95% CI for a population mean is (44.1 - 4.88 , 44.1 + 4.88)

(39.22, 48.98)

Since 37 does not lie in the 95% CI, we reject the null hypothesis that ?=37 . Answer is Yes

Since 48 lie in the 95% CI, we cannot reject the null hypothesis that ?=37 . Answer is No

In general, you fail to reject the null hypothesis if ? is IN the confidence interval.

2.

We use z test if:

• σ is known, and the sample size is at least 30 (for any population)
• σ is known, and the original population is normal (for any value of n)

The t-test should be used instead of the z-test if

A. ?>30 and ? is unknown

3.

If we have no knowledge of even the approximate value of the sample proportion ?̂ , we:
A. let ?̂ =0.50

so, as to estimate the largest sample size.