Question

Question 15 Find the p-value for the hypothesis test. A random sample of size 50 is taken. Type numbers in the boxes. The sample has a mean of 420 and a standard deviation of 81. 10 points Ho: u = 400 H.: u > 400 The p-value for the hypothesis test is Your answer should be rounded to 4 decimal places. Ouation 16

Answer 1

Solution :

This is the right tailed test .

The null and alternative hypothesis is ,

H₀ :  $\mu$ = 400

H_a : $\mu$ > 400

Test statistic = z

= ($\bar x$ - $\mu$ ) / $\sigma$ / $\sqrt$ n

= (420 - 400) / 81 / $\sqrt$ 50 = 1.746

Test statistic = 1.746

P(z > 1.746) = 1 - P(z < 1.746) = 1 - 0.9596 = 0.0404

P-value = 0.0404

null hypothesis is rejected