Question

Find the p -value for the hypothesis test. A random sample of size 50 is taken. The sample has a mean of 375 and a standard deviation of 81. H 0 : µ = 400 H a : µ< 400 The p -value for the hypothesis test is . Your answer should be rounded to 4 decimal places.

Answer 1

Solution :

$\mu$= 400

$\bar x$ =375

$\sigma$ =81

n = 50

This is the left tailed test .

The null and alternative hypothesis is ,

H₀ :  $\mu$ = 400

H_a : $\mu$     <400

Test statistic = z

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

= (375 -400) /81 / $\sqrt$ 50

= −2.18

P(z < −2.18 ) = 0.0146

P-value = 0.0146