Question

. To test H0: m = 105 versus H1: m ≠ 105, a simple random sample of size n = 35 is obtained. (a) Does the population have to be normally distributed to test this hypothesis by using the methods presented in this section? Why? (b) If x = 101.9 and s = 5.9, compute the test statistic. (c) Draw a t-distribution with the area that represents the P-value shaded. (d) Approximate and interpret the P-value. (e) If the researcher decides to test this hypothesis at the a = 0.01 level of significance, will the researcher reject the null hypothesis? Why?

Answer 1

Answer:

A.) No

B.) test statistic = - 3.108

Check explanation

Step-by-step explanation:

H0: m = 105 versus H1: m ≠ 105

Sample size, n = 35, since we have a large sample size, greater than 30.

B.)

xbar = 101.9 ; s = 5.9

Test statistic :

T = (xbar - μ) ÷ (s/√n)

T = (101.9 - 105) / (5.9/√35)

T = - 3.1 / 0.9972820

Test statistic = - 3.11

Pvalue from Tstatistic, df = 34

Pvalue = 0.003772( Pvalue calculator)

Pvalue is the probability of obtaining a value more extreme or exactly that of the test statistic.

At α = 0.01

Pvalue < α ; We fail to reject the Null