Question

A student at a university wants to determine if the proportion of students that use iPhones is less than 0.45. The hypotheses for this scenario are as follows. Null Hypothesis: p ? 0.45, Alternative Hypothesis: p < 0.45. If the student randomly samples 29 other students and finds that 10 of them use iPhones, what is the test statistic and p-value?

1)	Test Statistic: -1.138, P-Value: 0.127

2)	Test Statistic: -1.138, P-Value: 0.873

3)	Test Statistic: 1.138, P-Value: 0.127

4)	Test Statistic: 1.138, P-Value: 0.873

5)	Test Statistic: -1.138, P-Value: 0.254

Does the average internet speed of an ISP depend on continent? Specifically, you would like to test whether customers in North America have an average internet download speed that is greater than the average download speed of customers in Europe. If North American customers are in group 1 and European customers are in group 2, what are the hypotheses for your test of interest?

1)	HO: ?1 > ?2 HA: ?1 ? ?2

2)	HO: ?1 = ?2 HA: ?1 ? ?2

3)	HO: ?1 < ?2 HA: ?1 ? ?2

4)	HO: ?1 ? ?2 HA: ?1 > ?2

5)	HO: ?1 ? ?2 HA: ?1 < ?2

A new gasoline additive is supposed to make gas burn more cleanly and increase gas mileage in the process. Consumer Protection Anonymous conducted a mileage test to confirm this. They took a sample of their cars, filled it with regular gas, and drove it on I-94 until it was empty. They repeated the process using the same cars, but using the gas additive. Using the data they found, they performed a paired t-test with data calculated as (with additive - without additive) with the following hypotheses: Null Hypothesis: ?_D = 0, Alternative Hypothesis: ?_D ? 0. If they calculate a p-value of 0.0028 in the paired samples t-test, what is the appropriate conclusion?

1)	The average difference in gas mileage is equal to 0.

2)	The average difference in gas mileage is significantly less than 0. The average gas mileage was higher without the additive.

3)	We did not find enough evidence to say the average difference in gas mileage was not 0. The additive does not appear to have been effective.

4)	The average difference in gas mileage is significantly larger than 0. The average gas mileage was higher with the additive.

5)	The average difference in gas mileage is significantly different from 0. There is a significant difference in gas mileage with and without the additive.

Answer 1

a) p = 10/29 = 0.3448

z = (p - P)/sqrt(P(1 - P)/n)

   = (0.3448 - 0.45)/sqrt(0.45 * (1 - 0.45)/29)

   = -1.1387

P-value = P(Z < -1.1387)

              = 0.127

Option - 3) is correct.

b)Option - 4) H0 : <

                     HA : >

c) At 0.05 significance level, as the P-value is less than the significance level we should reject H₀.

Option - 5) The average difference in gas mileage is significantly different from 0. There is a significant difference in gas mileage with and without the additive.