Question

9.138 Consider a random sample of size 20 from a normal population with hypothesized mean 1.618. a. Write the four parts for a one-sided, left-tailed hypothesis test concerning the population mean with α 0.05. b. Suppose x = 1.5 and s = 0.45. Find the value of the test statistic, and draw a conclusion about the population mean. c. Find the p value associated with this hypothesis test.

Answer 1

a) (i)The null and alternative hypothesis

H0 : μ = 1.618

Ha : μ < 1.618

(ii)Test statistic

$t= \frac{\bar{X}-\mu }{s /\sqrt{n}}$

(iii)Critical value of t

At with 19 df ,

a-0.05

tc = -1.7291

(iv) Rejection region

If test statistic < -1.7291 we reject H0

(b) Test statistic

1.5 1.618 0.45/V20

= -1.173

since t is not in the rejection region

we fail to reject H0.

There is not sufficient evidence to conclude that population mean is less than 1.618.

(c) t = -1.173

df =19

P value = 0.12765