Question

# 1 Over the past several years, the proportion of one-person households has been increasing. The Census...

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.

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.

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