Question

In: Statistics and Probability

A study is made of residents in Phoenix and its suburbs concerning the proportion of residents...

A study is made of residents in Phoenix and its suburbs concerning the proportion of residents who subscribe to Sporting News. A random sample of

n1 = 88

urban residents showed that

10

subscribed, and a random sample of

n2 = 97

suburban residents showed that

19

subscribed. Does this indicate that a higher proportion of suburban residents subscribe to Sporting News? Use a 5% level of significance.

What are we testing in this problem?

paired differencedifference of means    single proportiondifference of proportionssingle mean

What is the level of significance?


State the null and alternate hypotheses.

H0: p1p2; H1: p1 < p2H0: p1 > p2; H1: p1p2    H0: p1p2; H1: p1 = p2H0: p1p2; H1: p1 > p2H0: p1 < p2; H1: p1p2H0: p1 = p2; H1: p1p2


What sampling distribution will you use? What assumptions are you making?

The standard normal. The number of trials is sufficiently large.The Student's t. The number of trials is sufficiently large.    The standard normal. We assume the population distributions are approximately normal.The Student's t. We assume the population distributions are approximately normal.


What is the value of the sample test statistic? (Test the difference p1p2). Round your answer to two decimal places.


Estimate the P-value.

P-value > 0.2500.125 < P-value < 0.250    0.050 < P-value < 0.1250.025 < P-value < 0.0500.005 < P-value < 0.025P-value < 0.005


Sketch the sampling distribution and show the area corresponding to the P-value.


Will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?

At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.    At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.


Interpret your conclusion in the context of the application.

There is sufficient evidence at the 0.05 level to conclude that the proportion of suburban residents subscribing to Sporting News is higher.There is insufficient evidence at the 0.05 level to conclude that the proportion of suburban residents subscribing to Sporting News is higher.    

Solutions

Expert Solution

Given that,

For urban residents : n1 = 88, x1 = 10 and

For suburban : n2 = 97, x2 = 19 and

Pooled proportion is,

This is difference of proportion test. (Two-proportion test).

Level of significance = 0.05

The null and alternative hypotheses are,

H0 : p1 ≥ p2

Ha : p1 < p2

The sampling distribution of the sample proportions is The standard normal. The number of trials is sufficiently large.

Test statistic is,

=> Test statistic = Z = -1.54

p-value = P(Z < -1.54) = 0.0618

0.050 < P-value < 0.125

Since, p-value is greater than 0.05, we fail to reject H0.

At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

​​​Conclusion : There is insufficient evidence at the 0.05 level to conclude that the proportion of suburban residents subscribing to Sporting News is higher.  

​​​​​​

​​​


Related Solutions

A study is made of residents in Phoenix and its suburbs concerning the proportion of residents...
A study is made of residents in Phoenix and its suburbs concerning the proportion of residents who subscribe to Sporting News. A random sample of n1 = 88urban residents showed that r1 = 13 subscribed, and a random sample of n2 = 99 suburban residents showed that r2 = 20 subscribed. Does this indicate that a higher proportion of suburban residents subscribe to Sporting News? Use a 5% level of significance. What are we testing in this problem? difference of...
A study is made of residents in Phoenix and its suburbs concerning the proportion of residents...
A study is made of residents in Phoenix and its suburbs concerning the proportion of residents who subscribe to Sporting News. A random sample of n1 = 88 urban residents showed that 10 subscribed, and a random sample of n2 = 99 suburban residents showed that 19 subscribed. Does this indicate that a higher proportion of suburban residents subscribe to Sporting News? Use a 5% level of significance. a.)What are we testing in this problem? -difference of proportions -single mean...
10. A study is made of residents in Phoenix and its suburbs concerning the proportion of...
10. A study is made of residents in Phoenix and its suburbs concerning the proportion of residents who subscribe to Sporting news. A random sample of 88 urban residents showed that 12 subscribed. A random sample of 97 suburban residents showed that 18 subscribed. Does this indicate that there is a difference in the proportion of suburban residents that subscribe to this magazine? Use alpha at .05. a. State the null and alternative hypotheses (.5 points) b. What is the...
In a study to estimate the proportion of residents in a certain city and its suburbs...
In a study to estimate the proportion of residents in a certain city and its suburbs who favor the construction of a nuclear power plant, it is found that 210 of 300 urban residents favor the construction while only 180 of 200 suburban residents are in favor. (a) Is there a significant difference between the proportion of urban and suburban residents who favor construction of the nuclear power plant? α=0.05. (b) Construct a 95% confidence interval for the difference of...
Suppose a government official in Phoenix, Arizona, wants to know what proportion of Phoenix residents are...
Suppose a government official in Phoenix, Arizona, wants to know what proportion of Phoenix residents are infected with the COVID-19 virus. Because of the limited availability of tests, she cannot test all the residents of Phoenix. A random sample of 180 Phoenix residents was taken, and these residents were tested for the virus. Of these 180 people, 36 were found to be infected with the virus. Find a 95% confidence interval for the true proportion of Phoenix residents who are...
1. The Tiebout model is supported by the fact that residents within metropolitan suburbs have ____...
1. The Tiebout model is supported by the fact that residents within metropolitan suburbs have ____ preferences and housing prices are generally _____ in communities with efficient A.similar/lower B.varied/higher C.varied/lower D.similar/higher 2. Welfare programs have ____ tax-benefit linkages. The Tiebout model suggests these programs should be offered at the _____ level. A.strong/local B.strong/national C.weak/local D.weak/national 3. National defense is best provided at the _____ level because ____. A.local/there are low economies of scale. B.national/there are strong tax-benefit linkages C.local/there are...
A recent study attempted to estimate the proportion of Florida residents who were willing to spend...
A recent study attempted to estimate the proportion of Florida residents who were willing to spend more tax dollars on protecting the Florida beaches from environmental disasters. Forty-six hundred Florida residents were surveyed. 37% of those surveyed said they were willing to spend more tax dollars on protecting the Florida beaches from environmental disasters. The researcher concludes that about 37% of all Florida residents were willing to spend more tax dollars on protecting the Florida beaches. 1. What is the...
Researchers are comparing the proportion of University Park students who are Pennsylvania residents to the proportion...
Researchers are comparing the proportion of University Park students who are Pennsylvania residents to the proportion of World Campus students who are Pennsylvania residents. Data from a sample are presented in the contingency table below. Primary Campus Total University Park World Campus Pennsylvania Resident Yes 115 70 185 No 86 104 190 Total 201 174 375 Construct a 95% confidence interval to estimate the difference between the proportion of all University Park students who are Pennsylvania residents and the proportion...
Manufacturer made two announcements concerning its common stock today.
11. Manufacturer made two announcements concerning its common stock today. First, the company announced that the next annual dividend will be $1.75 a share. Secondly, all dividends after that will decrease by 1.5 percent annually, What is t maximum you should pay to purchase the stock if you require a 14% return? A. $11.29 B.$12.64 C.$13.27 D.$14.00 E.$14.21 12. The common stock of Textile Mills pays an annual dividend of $1.65 a share. The Company has promised to maintain a constant dividend...
A town council wants to estimate the proportion of residents who are in favor of a...
A town council wants to estimate the proportion of residents who are in favor of a proposal to upgrade the computers in the town library. A random sample of 100 residents was selected, and 97 of those selected indicated that they were in favor of the proposal. Is it appropriate to assume that the sampling distribution of the sample proportion is approximately normal?
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT