Question

Many individuals over the age of 40 develop an intolerance for milk and milk-based products. A dairy has developed a line of lactose-free products that are more tolerable to such individuals. To assess the potential for these products, the dairy commissions a market research study of individuals over the age 40 in its sales area. A random sample of 150 individuals shows that 54 of them suffer from milk intolerance. Calculate and interpret the 95% confidence interval for the population proportion of individuals who suffer milk intolerance. According to your results, is it reasonable to conclude that the proportion of those who suffer milk intolerance is at most 44% of individuals over the age of 40? Please justify your answer.

Answer 1

H0: mu = 0.44
Ha: mu < 0.44

sample proportion, pcap = 0.36
sample size, n = 150
Standard error, SE = sqrt(pcap * (1 - pcap)/n)
SE = sqrt(0.36 * (1 - 0.36)/150) = 0.0392

For 0.95 Confidence level, the z-value = 1.96
CI = (xbar - z*SE, xbar + z*SE)
CI = (0.36 - 1.96 * 0.0392 , 0.36 + 1.96 * 0.0392)
CI = (0.2832 , 0.4368)

As the above CI does not include 0.44, we reject H0
There are significant evience to conclude that the proportion of those who suffer milk intolerance is at most 44%