Principle 2: When the confidence intervals in two different populations do not overlap, it is reasonable to conclude that the two populations are different.

1.Profitable Upgrade?Your company must charge $100 for a software upgrade to make a profit on its development.You must find out if your customers are willing to pay this much.A random sample of 80 customers finds that 23 would pay $100 for the upgrade.If the upgrade is to be profitable, you will need to sell it to more than 20% of your customers.Do the sample data provide good evidence that more than 20% are willing to buy at the 5% level of significance?

a)State the appropriate null and alternative hypotheses.Explain how you decided the alternative.

b)Give the z statistic and its p-value for this test.

c)Should you proceed with plans to develop and market the upgrade?Explain in context of this hypothesis test.

d)Give the 90% confidence interval for the proportion of all customers willing to pay $100.00 for the upgrade.Explain how this supports your hypothesis test conclusion.

e)Your company's overseas division also took a random sample of 50 customers and found that 38 would pay the $100.00 upgrade.Explain (Use Principal 2) why or why not these two populations are different.