Question

A psychologist is studying smokers' self-images, which she measures by the self-image (SI) score from a personality inventory. For adults in the U.S., the mean SI score from this inventory is about

145

.

The psychologist gathers a random sample of

17

SI scores of smokers and finds that their mean is

126

and their standard deviation is

34

. Assume that the population of SI scores of smokers is normally distributed with mean

μ

. Based on the sample, can the psychologist conclude that

μ

is different from

145

? Use the

0.1

level of significance.

Perform a two-tailed test. Then fill in the table below.

Carry your intermediate computations to at least three decimal places and round your answers as specified in the table. (If necessary, consult a list of formulas.)

The null hypothesis: H0: The alternative hypothesis: H1: The type of test statistic: (Choose one)ZtChi squareF The value of the test statistic: (Round to at least three decimal places.) The two critical values at the 0.1 level of significance: (Round to at least three decimal places.) and At the 0.1 level of significance, can the psychologist conclude that the mean SI score among smokers is different from 145?

Answer 1

Slotion:-

= 145

= 126

= 34

n = 17

This is the two tailed test .

The null and alternative hypothesis is

H0 :   = 145

Ha : 145

Test statistic = z

= ( - ) / / n

= (126 -145) /34 / 17

= -2.304

P (Z < -2.304 ) =0.0106*2 = 0.0212

P-value = 0.0212

= 0.10

The two tailed test critical value is = 1.645

0.0212 < 0.10

Reject the null hypothesis .

There is sufficient evidence to conclude that the mean SI score among smokers is different from

145.