Question

A statistician was testing the following hypothesis: Ho: u < 501.3 The p-value approach was to be used with a sigma of 32.2. A sample of size of 51 gave a sample mean of 505.2. Find the p-value to 4 decimal places.

Answer 1

this is the right tailed test .  

The null and alternative hypothesis is ,

H0 :  $\mu$ <=501.3

Ha : $\mu$ > 501.3

Test statistic = z

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

= (505.2-501.3) / 32.2 / $\sqrt$ 51

=0.86

P(z >0.86 ) = 1 - P(z <0.86 ) =1- 0.8051=0.1949 using z table

P-value = 0.1949