To test [tex]H_0: \mu = 40[/tex] versus [tex]H_1: \mu < 40[/tex], a random sample of size [tex]n=23[/tex] is obtained from a population that is known to be normally distributed. Complete parts (a) through (d) below.

(a) If [tex]\bar{x} = 37.9[/tex] and [tex]s = 11.8[/tex], compute the test statistic [tex]t_0[/tex].

(Round to three decimal places as needed.)

Question

High School

Answer :

SkylerBliss SkylerBliss · Answer 1 · 2023-10-08T13:44:49-04:00

The test statistic to test Hou = 40 versus H:1<40, given x=37.9 and s=11.8, is approximately -0.854.

To test the hypothesis Hou = 40 versus H:1<40, we need to compute the test statistic using the given information.

Given:

Sample mean (x) = 37.9 Sample standard deviation (s) = 11.8 Population mean (H0) = 40 Sample size (n) = 23

Using the formula for the test statistic:

t = (x - H0) / (s / sqrt(n))

Substituting the given values:

t = (37.9 - 40) / (11.8 / sqrt(23))

Calculating the test statistic:

t = -2.1 / (11.8 / 4.7958)

t = -2.1 / 2.4596

t ≈ -0.854

Therefore, the test statistic to test Hou = 40 versus H:1<40 is approximately -0.854.

Learn more about testing hypotheses here:

https://brainly.com/question/3963904

#SPJ11