Question

A random sample of n = 100 tenth graders indicated a mean reading rate of ¯ x = 154 words per minute withastandarddeviationof s =15wordsperminute. Usingthesedata,testtheclaimthatthemeanreading rate of tenth graders is 150 words per minute, using a significance level of α =0.05. Use the hypotheses H0 : µ =150 wpm and HA : µ 6=150 wpm Also, explicitly give the p-value associated to this hypothesis test.

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is ,

H₀ :   = 150

H_a :    150

Test statistic = z

= ( - ) / s / n

= (154 - 150) / 15 / 100

= 2.67

P(z > 2.67) = 1 - P(z < 2.67) = 0.0038

P-value = 0.0038