1
Over the past several years, the proportion of oneperson households has been increasing. The Census Bureau would like to test the hypothesis that the proportion of oneperson 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 socialnetworking 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 socialnetworking sites to screen job candidates during the hiring process. Assume that the actual proportion of organizations that use socialnetworking 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 socialnetworking 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 pvalue 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 oneway 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.
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(1p)/n)
substitute values
= (0.344  0.27)/sqrt(0.27(10.27)/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.
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