Question

A student at a university wants to determine if the proportion of students that use iPhones is different from 0.45. If the student conducts a hypothesis test, what will the null and alternative hypotheses be?

1)	HO: p ≤ 0.45 HA: p > 0.45

2)	HO: p > 0.45 HA: p ≤ 0.45

3)	HO: p = 0.45 HA: p ≠ 0.45

4)	HO: p ≠ 0.45 HA: p = 0.45

5)	HO: p ≥ 0.45 HA: p < 0.45

A USA Today article claims that the proportion of people who believe global warming is a serious issue is 0.79, but given the number of people you've talked to about this same issue, you believe it is less than 0.79. If you conduct a hypothesis test, what will the null and alternative hypotheses be?

1)	HO: p ≤ 0.79 HA: p > 0.79

2)	HO: p < 0.79 HA: p ≥ 0.79

3)	HO: p ≥ 0.79 HA: p < 0.79

4)	HO: p = 0.79 HA: p ≠ 0.79

5)	HO: p > 0.79 HA: p ≤ 0.79

Your friend tells you that the proportion of active Major League Baseball players who have a batting average greater than .300 is less than 0.62, a claim you would like to test. The hypotheses for this test are Null Hypothesis: p ≥ 0.62, Alternative Hypothesis: p < 0.62. If you randomly sample 29 players and determine that 22 of them have a batting average higher than .300, what is the test statistic and p-value?

1)	Test Statistic: 1.538, P-Value: 1.876

2)	Test Statistic: 1.538, P-Value: 0.938

3)	Test Statistic: -1.538, P-Value: 0.938

4)	Test Statistic: -1.538, P-Value: 0.062

5)	Test Statistic: 1.538, P-Value: 0.062

A student at a university wants to determine if the proportion of students that use iPhones is different from 0.4. The hypotheses for this scenario are as follows. Null Hypothesis: p = 0.4, Alternative Hypothesis: p ≠ 0.4. If the student randomly samples 26 other students and finds that 9 of them use iPhones, what is the test statistic and p-value?

1)	Test Statistic: -0.56, P-Value: 0.712

2)	Test Statistic: -0.56, P-Value: 0.575

3)	Test Statistic: 0.56, P-Value: 0.575

4)	Test Statistic: -0.56, P-Value: 0.425

5)	Test Statistic: -0.56, P-Value: 0.288

Answer 1

1) Option 3

H_O: p = 0.45
H_A: p ≠ 0.45

2) Option 3

H_O: p ≥ 0.79
H_A: p < 0.79

3) Option 5

Test Statistic: 1.538, P-Value: 0.062

P = 0.62

P = x / n = 22 / 29 = 0.7586

σ = sqrt[ P * ( 1 - P ) / n ] = sqrt [(0.62 * 0.38) / 29] = 0.0901
z = (p - P) / σ = (0.7586 - 0.62)/0.0901 = 1.538

For this p – value = P(Z > 1.538) = 0.652 (using normal distribution)

4) Option 5

Test Statistic: -0.56, P-Value: 0.288

P = 0.4

P = x / n = 9 / 26 = 0.3462

σ = sqrt[ P * ( 1 - P ) / n ] = sqrt [(0.4 * 0.6) / 26] = 0.0961
z = (p - P) / σ = (0.3462 – 0.4)/0.0961 = - 0.5598 = -0.56 (rounded to 2 decimals)

For this p – value = P(Z < -0.56) = 0.288 (using normal distribution)