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

H₀: = 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.