Two separate marketing teams, Team A and Team B, have each designed a 30 second advertisement for the new Cloak soft drink. The manager of marketing is interested to see if there is any difference between the effectiveness of the two ads.

A random sample of 50 people are shown the ad from Team A and asked if they would definitely buy the new drink. In this sample, 14 people said that they would. A second random sample of 50 people are shown the ad from Team B and asked if they would definitely buy the drink. In this sample, 11 people said that they would.

Let₁denote the population proportion of people that would definitely buy the drink if they saw the ad from Team A. Let₂denote the population proportion of people that would definitely buy the drink if they saw the ad from Team B.

A hypothesis test is conducted with the following hypotheses:

H₀:₁=₂

H_A:₁₂

The level of significance used in this test is 0.05. You may find thisstandard normal tableuseful.

a)Calculate the test statistic (z) for this test. Give your answer to 2 decimal places.

z =

b)In this test the null hypothesisisis notrejected.

Due to various socio-economic factors, residents of a particular city have an unusually high level of attendance at private schools. A study is conducted to determine whether there is any difference between the rate at which males and females choose private schools over public schools in this city.

A random sample of 75 males from the city are contacted and asked if they attend or ever attended a private school. The proportion that did (to 2 decimal places) is 0.56. Similarly, a random sample of 125 females from the city are contacted and asked the same question. The proportion that attended a private school (to 2 decimal places) is 0.60.

Let₁denote the population proportion of males that attended a private school. Similarly, let₂denote the population proportion of females that attended a private school.

Construct a 90% confidence interval for the difference between these two proportions(₁-₂). Give your answers to 3 decimal places. You may find thisstandard normal tableuseful.

₁-₂