7.11 Topic 11: Inference for Two Proportions 88. The Vegetarian Resource Group commissioned Harris Poll in 2016 to conduct a nationally rep- resentative online poll of 2,015 American adults aged 18 and over. They found that 3.3% of the respondents identified as vegetarian. Food habits in India tend to have a large religious and social component. How does the popularity of the vegetarian diet differ in the US and India? A 2014 survey conducted by the Registrar General of India found that 29% of Indians were vegetarian. Suppose the proportion was obtained from a random sample of 1,000 Indians. (a) Construct and interpret a 99% confidence interval for the difference in proportions of tarians in India and the US. vege- (b) Based on the interval, what kind of evidence do you expect to have for the alternative in a two-sided hypothesis test? Explain. 89. It is hard to persuade consumers to abandon a product with which they are familiar. One experiment gave consumers free samples of a new laundry detergent and also a standard detergent. After some time, ask the subjects which detergent they prefer. Here are the data. User Nonuser Prefer new product Prefer standard product 19 31 29 27 (a) Calculate a 90% confidence interval for the difference in proportions between nonusers and users of the standard detergent that prefer the new detergent. (b) Based on the confidence interval in (a), can we conclude that a significant difference exists between the proportion of nonusers of the standard detergent who prefer the new detergent and the proportion of users of the standard detergent who prefer the new detergent? Explain. 90. Spending on concessions at the movies varies by age of the movie goer. A random sample of 100 adults in their 40's found that 70 purchased popcorn. A random sample of 100 adults less than 40 years old found that 59 purchased popcorn. (a) State the hypotheses for determining of there is a difference in the proportion of adults who purchase popcorn in each age group. (b) Calculate the test statistic. (c) Calculate the p-value. (d) Interpret the p-value. (e) State your conclusion. (f) Would a confidence interval for the difference in proportions contain zero? Explain without constructing the interval. 91. Africa and the Middle East are two of the least popular regions traveled to in study abroad programs. Suppose a random sample of 250 college students found that 10 traveled to Africa for study abroad. A second random sample of 375 college students found that 10 studied in the Middle East. Is there evidence that more students study abroad in Africa than the Middle East? Perform the appropriate test and include all steps.

Question

Question 89 parts A and B 

7.11 Topic 11:
Inference for Two Proportions
88. The Vegetarian Resource Group commissioned Harris Poll in 2016 to conduct a nationally rep-
resentative online poll of 2,015 American adults aged 18 and over. They found that 3.3% of the
respondents identified as vegetarian.
Food habits in India tend to have a large religious and social component. How does the popularity
of the vegetarian diet differ in the US and India? A 2014 survey conducted by the Registrar
General of India found that 29% of Indians were vegetarian. Suppose the proportion was obtained
from a random sample of 1,000 Indians.
(a) Construct and interpret a 99% confidence interval for the difference in proportions of
tarians in India and the US.
vege-
(b) Based on the interval, what kind of evidence do you expect to have for the alternative in a
two-sided hypothesis test? Explain.
89. It is hard to persuade consumers to abandon a product with which they are familiar. One
experiment gave consumers free samples of a new laundry detergent and also a standard detergent.
After some time, ask the subjects which detergent they prefer. Here are the data.
User
Nonuser
Prefer new product
Prefer standard product
19
31
29
27
(a) Calculate a 90% confidence interval for the difference in proportions between nonusers and
users of the standard detergent that prefer the new detergent.
(b) Based on the confidence interval in (a), can we conclude that a significant difference exists
between the proportion of nonusers of the standard detergent who prefer the new detergent
and the proportion of users of the standard detergent who prefer the new detergent? Explain.
90. Spending on concessions at the movies varies by age of the movie goer. A random sample of 100
adults in their 40's found that 70 purchased popcorn. A random sample of 100 adults less than
40 years old found that 59 purchased popcorn.
(a) State the hypotheses for determining of there is a difference in the proportion of adults who
purchase popcorn in each age group.
(b) Calculate the test statistic.
(c) Calculate the p-value.
(d) Interpret the p-value.
(e) State your conclusion.
(f) Would a confidence interval for the difference in proportions contain zero? Explain without
constructing the interval.
91. Africa and the Middle East are two of the least popular regions traveled to in study abroad
programs. Suppose a random sample of 250 college students found that 10 traveled to Africa
for study abroad. A second random sample of 375 college students found that 10 studied in the
Middle East. Is there evidence that more students study abroad in Africa than the Middle East?
Perform the appropriate test and include all steps.
Expand
Transcribed Image Text

7.11 Topic 11: Inference for Two Proportions 88. The Vegetarian Resource Group commissioned Harris Poll in 2016 to conduct a nationally rep- resentative online poll of 2,015 American adults aged 18 and over. They found that 3.3% of the respondents identified as vegetarian. Food habits in India tend to have a large religious and social component. How does the popularity of the vegetarian diet differ in the US and India? A 2014 survey conducted by the Registrar General of India found that 29% of Indians were vegetarian. Suppose the proportion was obtained from a random sample of 1,000 Indians. (a) Construct and interpret a 99% confidence interval for the difference in proportions of tarians in India and the US. vege- (b) Based on the interval, what kind of evidence do you expect to have for the alternative in a two-sided hypothesis test? Explain. 89. It is hard to persuade consumers to abandon a product with which they are familiar. One experiment gave consumers free samples of a new laundry detergent and also a standard detergent. After some time, ask the subjects which detergent they prefer. Here are the data. User Nonuser Prefer new product Prefer standard product 19 31 29 27 (a) Calculate a 90% confidence interval for the difference in proportions between nonusers and users of the standard detergent that prefer the new detergent. (b) Based on the confidence interval in (a), can we conclude that a significant difference exists between the proportion of nonusers of the standard detergent who prefer the new detergent and the proportion of users of the standard detergent who prefer the new detergent? Explain. 90. Spending on concessions at the movies varies by age of the movie goer. A random sample of 100 adults in their 40's found that 70 purchased popcorn. A random sample of 100 adults less than 40 years old found that 59 purchased popcorn. (a) State the hypotheses for determining of there is a difference in the proportion of adults who purchase popcorn in each age group. (b) Calculate the test statistic. (c) Calculate the p-value. (d) Interpret the p-value. (e) State your conclusion. (f) Would a confidence interval for the difference in proportions contain zero? Explain without constructing the interval. 91. Africa and the Middle East are two of the least popular regions traveled to in study abroad programs. Suppose a random sample of 250 college students found that 10 traveled to Africa for study abroad. A second random sample of 375 college students found that 10 studied in the Middle East. Is there evidence that more students study abroad in Africa than the Middle East? Perform the appropriate test and include all steps.

Expert Answer

Want to see the step-by-step answer?

Check out a sample Q&A here.

Want to see this answer and more?

Experts are waiting 24/7 to provide step-by-step solutions in as fast as 30 minutes!*

*Response times may vary by subject and question complexity. Median response time is 34 minutes for paid subscribers and may be longer for promotional offers.
Tagged in
Math
Statistics

Related Statistics Q&A

Find answers to questions asked by students like you.

Q: Use une sampie data amo commdence lever given below to compiete pans (aj uroug u. A research institu...

A: Click to see the answer

Q: Sound Intensity The table lists intensities of sounds as multiples of a basic reference sound. A sca...

A: In this case, we need to construct the scatterplot for linear, quadratic, logarithmic, exponential, ...

Q: The article “Treadmill Exercise and Resistance Training in Patients With Peripheral Arterial Disease...

A: The claim is that the mean distance walked for patients using a treadmill is greater than the mean f...

Q: Standard Error of Estimate A random sample of 118 different female statistics students is obtained a...

A: The data show the statistics of 118 different female students paired weights (weight in kg, weight i...

Q: Question 77 parts C and D

A: Solution:  The sampling distribution of the sample proportion of females in samples of size 200 at t...

Q: Question 83 Parts A and B

A: Solution: It is required to fill in the blanks for the given questions. (a) The hypotheses are alway...

Q: Author’s Computer Files The author recorded the leading digits of the sizes of the electronic docume...

A:  

Q: Explained Variation Given that the linear correlation coefficient r is found to be 0.499, what is th...

A: It is given that the correlation coefficient(r) is 0.499. The coefficient of determination shows the...

Q: Express Courier Service has found that the delivery time for packages is normally distributed, with ...

A: Solution: It is given:  

Q: Let X - Poisson(1). Show that if x is a positive integer, then a. P(X = x) P(X = x- 1) x Show that i...

A: a)

Q: Predicting Nicotine in Cigarettes Refer to Data Set 13 “Cigarette Contents” in Appendix B and use th...

A: Note: Thanks for posting the question. We are using the Minitab software to predicting the nicotine ...

Q: The cost of 5 gallons of ice cream has a standard deviation of 7 dollars with a mean of 39 dollars d...

A: Click to see the answer

Q: Among the adults in a large city, 30% have a college degree. A simple random sample of 100 adults is...

A: Click to see the answer

Q: 7.3.29-1| Question Help A student wants to estimate the mean score of all college students for a par...

A: Solution: From the given information, the possible scores range from 200 to 1000. Here, the largest ...

Q: 22. Determine what the key terms below refer to in the following study. (6pts) We want to know the p...

A: Solution: Note: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-pa...

Q: Question 80 parts A, B, and C

A: Click to see the answer

Q: A recent television news station reports that the average Body Mass Index (BMI) (a measure of a pers...

A: Click to see the answer

Q: Grandma is trying out a new recipe for raisin bread. Each batch of bread dough makes three loaves, a...

A:   The Poisson distribution formula is,

Q: The article “Wind-Uplift Capacity of Residential Wood Roof-Sheathing Panels Retrofitted with Insulat...

A: The claim is that 6-inch spacing provides a higher mean failure pressure. The hypotheses can be cons...

Q: In 2001, one county reported that among 3132 white women who had babies, 94 were multiple births. Th...

A: The provided data is,

Q: Assume that the sample is a simple random sample obtained from a normally distributed population of ...

A: Click to see the answer

Q: An IQ test is designed so that the mean is 100 and the standard deviation is 16 for the population o...

A: Click to see the answer

Q: Suppose a 90 percent confidence interval to estimate a population proportion was calculated from a s...

A: Click to see the answer

Q: The number of large cracks in a length of pavement along a certain street has a Poisson distribution...

A: Click to see the answer

Q: Why is the Method of Moments estimator, in mathematical statistics, consistent?

A: Given that:  Method of Moments estimator, in mathematical statistics:

Q: Assume that IQ scores are normally distributed, with a standard deviation of 12 points and a mean of...

A: Click to see the answer

Q: Colonoscopy is a medical procedure that is designed to find and remove precancerous lesions in the c...

A: Click to see the answer

Q: Refer to the accompanying data display that results from a sample of airport data speeds in Mbps. Co...

A: a. You have already provided the confidence interval in the interval format, as: Tinterval - (13.046...

Q: A scientist computes a 90% confidence interval to be (4.38, 6.02). Using the same data, she also com...

A: Click to see the answer

Q: The April rainfall in Flagstaff, Arizona, follows a uniform distribution between 0.5 and 3.00 inches...

A: Click to see the answer

Q: True or false: a) If we reject H0, then we conclude that H0 is false. b) If we do not reject H0, the...

A: Click to see the answer

Q: 7.3.28-T E Question Help In order to estimate the mean amount of time computer users spend on the in...

A: Given that, Margin error=15 Standard deviation=195 95% confidence interval,

Q: Below indicate whether the appropriate test would be an independent t-test, dependent t-test, One-wa...

A: Click to see the answer

Q: Do Men Talk Less Than Women? Refer to Data Set 24 “Word Counts” and use the measured word counts fro...

A: The data shows the word counts for men and women and the level of significance is α=0.05. Assume tha...

Q: what is the value of Z if 75% percent of all possible z values (symmetrically distributed around the...

A: 75% percent of all possible z values are symmetrically distributed around the mean . Value of z is g...

Q: A large tank of fish from a hatchery is being delivered to a lake. The hatchery claims that the mean...

A: Consider X be a random variable which follows normal distribution indicates the length of fish in th...

Q: A random sample of n=4 scores is selected from a population with mu=80 and standard deviation=20. On...

A: Click to see the answer

Q: 2. A psychologist was looking at the effects of an intervention on depression levels. Three groups w...

A: The hypotheses for the given problem is given below:

Q: A crayon manufacturer is comparing the effects of two kinds of yellow dye on the brittleness of cray...

A: a. A crayon manufacturer is compares the effects of two kinds of yellow dye on the brittleness of cr...

Q: Question 86 parts A, B, and C

A: Click to see the answer

Q: Baseball Player Births In his book Outliers, author Malcolm Gladwell argues that more baseball playe...

A: Click to see the answer

Q: Question 83 parts C and D

A: Click to see the answer

Q: It is desired to check the calibration of a scale by weighing a standard 10-gram weight 100 times. L...

A: Click to see the answer

Q: A random sample of n = 9 is obtained from a normal distribution with μ= 40 and σ=15. What is the pro...

A: Click to see the answer

Q: The number of cars arriving at a given intersection follows a Poisson distribution with a mean rate ...

A: From the given information, Consider, X be a random variable that shows the number of cars arriving ...

Q: what is the probability to win buying one ticket at the lottery with 6 out of 56 balls and how many ...

A: Click to see the answer

Q: Several million lottery tickets are sold, and 60% of the tickets are held by women. Five winning tic...

A: a) Obtain the probability that less than equals to 3 winners will be women. Probability (That a tick...

Q: Are Seat Belts Effective? A simple random sample of front-seat occupants involved in car crashes is ...

A: a. The test hypotheses are: Null hypothesis: H0: p1 = p2 Alternative hypothesis: Ha: p1 > p2. Tes...

Q: A crossover trial is a type of experiment used to compare two drugs. Subjects take one drug for a pe...

A: Click to see the answer

Q: Amelia ran 2/3 of a mile each day for 5 days. How far did she run total?

A: Click to see the answer