Question

A random sample of 10 observations was drawn from a large normally distributed population. The data is below.

21, 22, 19, 25, 19, 19, 21, 26, 21, 23   

Test to determine if we can infer at the 3% significance level that the population mean is not equal to 22, filling in the requested information below.

A. The value of the standardized test statistic:

Note: For the next part, your answer should use interval notation. An answer of the form (−∞,a) is expressed (-infty, a), an answer of the form (b,∞) is expressed (b, infty), and an answer of the form (−∞,a)∪(b,∞) is expressed (-infty, a)U(b, infty).

B. The rejection region for the standardized test statistic:

C. The p-value is

D. Your decision for the hypothesis test:

A. Reject H1.
B. Reject H0.
C. Do Not Reject H1.
D. Do Not Reject H0.

Answer 1

= 21.6

s = 2.46

H₀: = 22

H₁: 22
A) The test statistic t = ()/(s/)

                            = (21.6 - 22)/(2.46/)

                            = -0.51

B) At alpha = 0.03, the critical values are t^* = +/- 2.574

Reject H₀, if t < -2.574 or t > 2.574

c) P-value = 2 * P(T < -0.51)

                 = 2 * 0.3112 = 0.6224

D) Since the test statistic value is not less than the lower critical value (-0.51 > -2.574), so we should not reject the null hypothesis.

Option - D) Do not reject H₀.