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Question: The Interactive Advertising Bureau surveyed a

The Interactive Advertising Bureau surveyed a representative sample of 1000 adult Americans and a representative sample of 1000 adults in China (“majority of Digital Users in U.S. and china regularly Shop and purchase via e-commerce,” november 10, 2016, www.iab.com, retrieved December 15, 2016). They reported that American shoppers are much more likely to use a credit or a debit card to make an online purchase. This conclusion was based on finding that 63% of the people in the United States sample said they pay with a credit or a debit card, while only 34% of those in the China sample said that they used a credit card or a debit card to pay for online purchases. To determine if the stated conclusion is justified, you want to carry out a test of hypotheses to determine if there is convincing evidence that the proportion who pay with a credit card or a debit card is greater for adult Americans than it is for adult Chinese. a. What hypotheses should be tested to answer the question of interest? b. Are the two samples large enough for the large-sample test for a difference in population proportions to be appropriate? Explain. c. Based on the following Minitab output, what is the value of the test statistic and what is the value of the associated P-value? If a significance level of 0.01 is selected for the test, will you reject or fail to reject the null hypothesis?
The Interactive Advertising Bureau surveyed a representative sample of 1000 adult Americans and a representative sample of 1000 adults in China (“majority of Digital Users in U.S. and china regularly Shop and purchase via e-commerce,” november 10, 2016, www.iab.com, retrieved December 15, 2016). They reported that American shoppers are much more likely to use a credit or a debit card to make an online purchase. This conclusion was based on finding that 63% of the people in the United States sample said they pay with a credit or a debit card, while only 34% of those in the China sample said that they used a credit card or a debit card to pay for online purchases. To determine if the stated conclusion is justified, you want to carry out a test of hypotheses to determine if there is convincing evidence that the proportion who pay with a credit card or a debit card is greater for adult Americans than it is for adult Chinese. 
a. What hypotheses should be tested to answer the question of interest?
b. Are the two samples large enough for the large-sample test for a difference in population proportions to be appropriate? Explain. 
c. Based on the following Minitab output, what is the value of the test statistic and what is the value of the associated P-value? If a significance level of 0.01 is selected for the test, will you reject or fail to reject the null hypothesis?


Difference = p (1) - p (2) 
Estimate for difference: 0.29 
95% lower bound for difference: 0.254818 
Test for difference = 0 (vs > 0): Z = 12.98 
P-Value = 0.000 
d. Interpret the result of the hypothesis test in the context of this problem.

Difference = p (1) - p (2) Estimate for difference: 0.29 95% lower bound for difference: 0.254818 Test for difference = 0 (vs > 0): Z = 12.98 P-Value = 0.000 d. Interpret the result of the hypothesis test in the context of this problem.





Transcribed Image Text:

Test and CI for Two Proportions Sample X N Sample p 1 630 1000 0.630000 2 340 1000 0.340000


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> USA TODAY (february 17, 2011) reported that 10% of 1008 American adults surveyed about their use of e-mail said that they had ended a relationship by e-mail. You would like to use this information to estimate the proportion of all adult Americans who hav

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> Researchers carried out an experiment to evaluate the effectiveness of using acupuncture to treat heel pain. The experiment is described in the paper “effectiveness of trigger point Dry needling for plantar heel pain: a randomized controlled trial” (Phys

> Many fundraisers ask for donations using e-mail and text messages. The paper “now or never! the effect of Deadlines on charitable giving: evidence from two natural field experiments” (Journal of Behavioral and Experimental Economics [2016]: 1–10) describ

> In a test of hypotheses about a difference in treatment proportions, what does it mean when the null hypothesis is not rejected?

> The report “Audience Insights: Communicating to Teens (Aged 12–17)” (2009, www.cdc.gov) described teens’ attitudes about traditional media, such as TV, movies, and newspapers. In a representative sample of American teenage girls, 41% said newspapers were

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> The news release referenced in the previous exercise also included data from independent samples of teenage drivers and parents of teenage drivers. In response to a question asking if they approved of laws banning the use of cell phones and texting while

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> The article “americans Say no to electric cars Despite gas prices” (USA TODAY, may 25, 2011) describes a survey of public opinion on issues related to rising gas prices. The survey was conducted by Gallup, a national p

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> Example 11.1 describes a study in which 354 of 708 people in the sample of 18- to 29-year-olds and 412 of the 1029 people in the sample of 30- to 49-year-olds said that they thought it was OK to use a cell phone in a restaurant. Note that the sample size

> An article titled “tcU horned frogs game preview (part 1)” (www.uwdawgpound.com/2016/11/26/13710900 /washington-huskies-tcu-horned-frogs-game-preview-part-1, retrieved December 20, 2016) previews a college basketball g

> Researchers were interested in comparing regular- intensity exercise and high-intensity exercise for patients recovering from hospitalization due to chronic obstructive pulmonary disease (COPD). The researchers followed patients in Denmark who were enrol

> Example 11.3 describes the results of a survey of 1129 full-time college faculty and 293 part-time college faculty. Survey participants were asked if they require undergraduate students to submit papers through plagiarism-detection software; 40% of the f

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> The article referenced in the previous exercise also indicated that 811 of the 1001 students surveyed said that they would feel restricted if they could only work on digital devices. Would a 95% confidence interval for the proportion of students age 13 t

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> Appropriate use of the interval requires a large sample. For each of the following combinations of n and p ˆ, indicate whether the sample size is large enough for this interval to be appropriate. a. n = 50 and p ˆ = 0.30 b. n =

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