Question

To test Upper H 0: mu equals20 versus Upper H 1: mu less than20, a simple random sample of size n=17 is obtained from a population that is known to be normally distributed.

(a) If

x overbar x equals=18.1

and s equals=4.1,

compute the test statistic.

t equals=−1.91

(Round to two decimal places as needed.)

c) Approximate the P-value. Choose the correct range for the P-value below.

A. 0.10 less than Upper P dash value less than 0.15

B. 0.15 less than Upper P dash value less than 0.20

C. 0.05 less than Upper P dash value less than 0.10

D. 0.025 less than Upper P dash value less than 0.05

Answer #1

H_{0}: = 20

H_{a} : < 20

Here,

= 18.1

s = 4.1

n= 17

standard error = s/sqrt(n) = 4.1/sqrt(17) = 0.995

t = (18.1 - 20)/0.995 = -1.91

(c) here as dF = n - 1 = 17 -1 = 16and so here we see the values from the t table

so here. we see t_{0.05,16} = -1.746

t_{0.025, 16} = -2.120

so here the p - value is in between 0.025 and 0.05 so here option D is correct.

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