Question

9. Use a significance level of a = 0.05 to test the claim that p = 32.6. The sample consists of 15 scores for which x = 40.8 and s = 7.9. a) State the hypotheses and label the claim. b) State the significance level (a). c) Is the test left-tailed, right-tailed, or two-tailed (circle one)? d) What is the critical value(s)? e) What are the P-value and test-statistic? f) State the conclusion.

Answer 1

a) Hypothesis : $H_0:\mu=32.6$ ( Claim ) VS $H_a:\mu\neq32.6$

b) Signiifcance level=

= 0,05

c) The test is two-tailed test.

because yje alternative hypothesis is not equal to type

d) The critical value is ,

$t_{n-1,\alpha/2}=t_{15-1,0.05/2}=\pm 2.145$ ; From t-table

e) The test statistic is ,

$t_{stat}=\frac{\bar{X}-\mu_0}{s/\sqrt{n}}=\frac{40.8-32.6}{7.9/\sqrt{15}}=4.021$

the p-value is ,

p-value=$P(t_{d.f.}>|t_{stat}|)=P(t_{14}>4.0201)=0.0013$

The Excel function is , =TDIST(4.0201,14,2)

f) Decision : Here , p-value=0.0013 <

= 0,05

Therefore , reject Ho.

Conclusion : Hence , there is not sufficient evidence to support the claim.