Question

A ketchup company regularly receives large shipments of tomatoes. For quality control purposes, they take a sample of tomatoes from each shipment. If the sample shows convincing evidence that more than 8\%8%8, percent of the tomatoes in the entire shipment are bruised, then the company will request a new shipment of tomatoes. So the company tests H0 : p = 0.08 versus Ha ​: p > 0.08H, where p is the proportion of tomatoes in the entire shipment that are bruised.
One day, a supervisor takes a random sample of 600 tomatoes from a shipment and finds that 53 of the tomatoes are bruised, which results in a test statistic of z ≈ 0.75. Assuming that the necessary conditions are met, what is the approximate P-value associated with the significance test for this shipment?

Answer 1

Answer:

The value is   $p-value = 0.22663$

Step-by-step explanation:

From the question we are told that

    The proportion of bruised tomatoes p =  0.08

    The  null hypothesis is  $H_o : p = 0.08$

    The alternative hypothesis is  $H_a : p > 0.08$

    The sample size is  n  =  600

    The number of bruised tomatoes from the sample selected is  k  =  53

    The test statistics is  z =0.75

Generally the p-value is mathematically represented as

      $p-value = P(Z > z)$

=>    $p-value = P(Z > 0.75)$

From the z-table  

    $P(Z > 0.75) = 0.22663$

So  

    $p-value = 0.22663$