Question

Assume that IQ scores for a certain population are approximately normally distributed. TotestH0 :μ=110againstH1 :μ̸=110,wetakearandomsampleofsizen=16from this population and observe x ̄ = 113.5 and s = 10. Do the test with significance level α = 0.05.

(a) Find the test statistic.
(b) Find the critical value from the t-table. (c) Do we accept or reject H0?

(d) Construct the confidence interval related to the test. What is your decision based on the confidence interval?

Answer 1

Solution :

= 110

=113.5

s =10

n = 16

This is the two tailed test .

The null and alternative hypothesis is ,

H₀ :    = 110

H_a :     110

a ) Test statistic = t

= ( - ) / s / n

= (113.5 - 110) / 10 / 16

= 1.4

Test statistic = t = 1.4

b ) The significance level is α =0.05, and the critical value for a two-tailed test is t_c​ = 2.131

P-value = 0.1819

= 0.05  

P-value ≥

0.1819 ≥ 0.05

c ) The null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that the population mean μ is different than 110, at the 0.05 significance level

d ) The 95% confidence interval is 108.171 < μ <118.829

The P-value approach: The p-value is p = 0.1819, and since p = 0.1819 ≥ 0.05