Question

​

Consider the following hypotheses and sample data, and then complete parts a and b below using a = 0.05. Ho:us 16 H: > 16 21 21 10 20 22 16 23 17 17 24

a) What conclusion should be​ drawn?

Determine the critical​ value(s).

The critical​ value(s) is(are)

b)Determine the test​ statistic,

tx.

c)

d) Use technology to determine the​ p-value for this test.

Answer 1

Solution Given data 21, 21, 10, 20, 24, 28, 16, 23,17,17 N=10 Null hypothesis Ho : ME 16 Alternativelypothesis Hi: >16 It is "right-tailed" test L=0.05 Now to find the sample mean : X = X 214 21+ 10 + 20+ 24 + 22 +16+23+17+17 X= 10 191 lo x = 19.1 * Now to find the Standard deviation 2 5= I(xi-x) N-1 (21-19)'+ (21–191)?+ (10-12-) (do -19.5+ (24 -1•) (22-11-2) + (16-19.1) ²4 (23-19.1) ²+ (17-1901) ²7 (17-19-1) ² 10-1 156.9 5= 9

5= 17.4333 s = 4.1753 Now to find the critical Value Here -n-1 degrees of freedom of = 10-1 df = 9 t critical value at &,df 0.05, 9 1.833 = 1.833 The critical value is (b) Now to determine the test statistic, tx We know that The formula of test Statistic, it is given by t = X-M X slun 19.1-16 4.1753 | Vio t 3.1 t 1.3203 t= 2.35 = 2.35

(c) Decision Test statistic > tcritical value 0.05 So we 2.35 > 1.833 Since the test statistic value is greater than t critical Value reject the nutt hypothesis (Ho) at level of significance Conclusion: Reject Ho. There is sufficient evidence to conclude that "> 16 Therefore the loption -B" is the correct answer. (d) Now to find the P-value P-value = 0.022 P-value = 0.022