A company believes that it controls more than 30 of the tota

A company believes that it controls more than 30% of the total market share for one of its products. To prove this belief, a random sample of 144 purchases of this product is contacted. It is found that 50 of the 144 purchased this company\'s brand of the product. If a researcher wants to conduct a statistical test for this problem, the observed z value would be _______.

Solution

so, here the population proportion = 30 / 100 = 0.3......
n= 144......population s.d = sqrt [ 0.3 * 0.7 / 144 ] = 0.03818813...........sample proportion = 50 / 144 =  0.347222....

so, observed z-value =  (0.347222 - 0.3) / 0.03818813 = 1.236562......