Question

1

Over the past several years, the proportion of one-person households has been increasing. The Census Bureau would like to test the hypothesis that the proportion of one-person households exceeds 0.27. A random sample of 125 households found that 43 consisted of one person. The Census Bureau would like to set α = 0.05. Use the critical value approach to test this hypothesis. Explain.

2

Organizations are relying more and more on social-networking sites to research job candidates. According to a 2018 CareerBuilder survey, 70% of employers use social media to screen job candidates during the hiring process. A random sample of 160 organizations found that 103 of them use social-networking sites to screen job candidates during the hiring process. Assume that the actual proportion of organizations that use social-networking sites to screen job candidates during the hiring process is 0.60. Calculate the probability of a Type II error when testing the hypothesis that less than 70% of organizations use social-networking sites to screen job candidates during the hiring process with α = 0.01.

3

The Wall Street Journal reported that there is evidence that Mac users are shown more expensive hotel prices when using Orbitz than PC users. Perform a hypothesis test to determine if the average hotel price for Mac users on Orbitz is higher than for PC users. The following data summarizes the sample statistics for hotel prices provided to each type of user from Orbitz. Assume that the population variances are equal.

	Mac	PC
Sample mean	$145	$116
Sample size	20	17
Sample standard deviation	$35	$32

Define Population 1 as Mac users and Population 2 as PC users and use the p-value approach to test this hypothesis with α = 0.01.

4

A car dealership would like to test the hypothesis that a difference exists in the city gas mileage (miles per gallon when driven in the city) of three cars, Honda Insight, Hyundai Ioniq and Toyota Camry. The following data represent the miles per gallon for a random sample of Honda Insight, Hyundai Ioniq and Toyota Camry cars.

Honda Insight	Hyundai Ioniq	Toyota Camry
40	35	35
36	37	34
37	38	31
38	34	36
38	34	33
36	36	35

Use Excel to perform a one-way ANOVA and state your conclusion using α = 0.05.

5

Brian plays golf regularly and would like to test the hypothesis that the number of golf balls that he loses during a round follows the Poisson distribution with an average of 2.0 balls per round. To test this hypothesis, he has collected the following lost ball data from a random sample of rounds.

Number of Lost Balls Per Round	Frequency
0	8
1	24
2	11
3	5
4	2

Perform this hypothesis test using α = 0.05.

6

Expedia would like to test the hypothesis that the standard deviation for the roundtrip airfare between Philadelphia and Paris is higher for a flight originating in Philadelphia when compared to a flight originating in Paris. The following data summarizes the sample statistics for roundtrip flights originating in both cities.

	Originating City
	Philadelphia	Paris
Sample standard deviation	$270	$240
Sample size	15	19

Test the hypothesis using α = 0.05.

7

The Marseille Water Taxi ferries tourists from the harbor at Marseille, France, to the Frioul Islands in the Mediterranean Sea. The table below shows the number of passengers on the noontime ferry over seven randomly selected days along with the current ambient temperature in degrees Celsius.

Temperature	Passengers
16	15
19	20
22	20
26	22
18	10
24	18

Use the Marseille Water Taxi data to calculate the 95% prediction interval for the number of passengers on a day when the ambient temperature is 23 degrees Celsius.

8

Delmarva Power is a utility company that would like to predict the monthly heating bill for a household in Kent County during the month of January. A random sample of 18 households in the county were selected and their January heating bill recorded. This data is shown in the table below along with the square footage of the house (SF), the age of the heating system in years (Age,) and the type of heating system (heat pump = 1 or natural gas = 0).

Household	Bill	SF	Age	Type
1	$255	2,070	7	Natural Gas
2	$286	1,909	17	Natural Gas
3	$296	2,004	8	Natural Gas
4	$300	2,307	22	Natural Gas
5	$305	3,021	5	Natural Gas
6	$317	2,683	14	Natural Gas
7	$321	1,511	8	Natural Gas
8	$321	2,836	3	Natural Gas
9	$339	2,553	20	Natural Gas
10	$349	2,497	11	Natural Gas
11	$369	2,103	12	Heat Pump
12	$374	2,486	18	Heat Pump
13	$381	2,279	19	Heat Pump
14	$413	2,477	17	Heat Pump
15	$419	3,218	11	Heat Pump
16	$441	3,080	8	Heat Pump
17	$522	2,507	20	Heat Pump
18	$560	3,517	18	Heat Pump

Determine and Interpret the meaning of the regression coefficients for the heating bill model.

Answer 1

Answer:

1.

Given,

Null hypothesis Ho : p = 0.27

Alternative hypothesis Ha : p > 0.27

x = 43

sample n = 125

sample proportion p^ = x/n

substitute values

= 43/125

= 0.344

consider,

test statistic z = (p^ - p)/sqrt(p(1-p)/n)

substitute values

= (0.344 - 0.27)/sqrt(0.27(1-0.27)/125)

z = 1.864

P value = P(z > 1.864)

= 0.0311609 [since from z table]

= 0.0312

Here we observe that, p value < alpha(0.05) , so we reject null hypothesis Ho.

So we conclude that, we have enough evidence to support the claim.