In June 2013, the mayor of New York City proposed a limit of at most 16 ounces o

Question

In June 2013, the mayor of New York City proposed a limit of at most 16 ounces on sugary beverages sold in restaurants. He argued that limiting sugar intake would lower rates of obesity and diabetes.   A Gallup poll used a random sample of 1015 US adults on June 15-16. They asked if people support a ban on sugary beverages with over 16 ounces in restaurants. Only 485 respondents said they favored the ban.  

Question 1 (1 point)

Check the three assumptions. Select all the assumptions which are satisfied.

Question 1 options:

Independent trials.

Large enough sample size?

Representative sample.

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Question 2 (1 point)

We want to know if less than half of US adults residents favor the ban. What are our null and alternative hypotheses?

Question 2 options:

H0:p=0.5,HA:p<0.478

H0:p =0.478,HA:p >0.478

H0:p =0.5,HA:p <0.5

H0:p=0.5,HA:p<0.5

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Question 3 (1 point)

Compute the observed result for this sample.

Question 3 options:

0.478

1015

0.5

485

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Question 4 (1 point)

Compute the standard error of the sample proportion under the null hypothesis.

Question 4 options:

0.478×0.5221015=0.01568

0.478×0.522485=0.02268

0.5×0.51015=0.01569

0.5×0.5485=0.02270

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Question 5 (2 points)

a) Copy down your answer choices to problems #3 and #4. Compute the z statistic. Must show your work to receive any credit! (1pt)

b) Use the web app to find the p-value. (1pt)

Question 5 options:

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Question 6 (1 point)

What distribution should you use as a reference to obtain a p-value?

Question 6 options:

t with 484 degrees of freedom

Normal

t with 1 degree of freedom

t with 1014 degrees of freedom

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Question 7 (1 point)

Explain how you used the web app to get the p-value for this test.

Question 7 options:

Less than the observed result.

Less than the null value.

Less than the z statistic.

Less than the standard error.

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Question 8 (1 point)

What do you “decide” about the null hypothesis using a 0.05 significance level?

Question 8 options:

Accept the null hypothesis.

Fail to accept the null hypothesis.

Reject the null hypothesis.

Fail to reject the null hypothesis.

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Question 9 (1 point)

Give your conclusion in the context of the problem.

Question 9 options:

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Question 10 (1 point)

To whom does your inference apply?  

Question 10 options:

The 1015 people in our sample

All US adults in June 2013

All New York City residents

All US adults

Independent trials.

Large enough sample size?

Representative sample.

Explanation / Answer

1.

   
Independent trials. [Check, as a random sam ple is used]
   
Large enough sample size [check, as 1016 is large]
   
Representative sample [Check, as it is a random sample]

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2.

Formulating the null and alternatuve hypotheses,          
          
Ho:   p   =   0.5
Ha:   p   <   0.5 [ANSWER, D]

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3.

As we see, the hypothesized po =   0.5      

Getting the point estimate of p, p^,          
          
p^ = x / n =    0.477832512 = 0.478 [ANSWER, A]

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4.      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.015694121 [ANSWER, A]

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5.      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    -1.412470846   [ANSWER]

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As this is a    1   tailed test, then, getting the p value,  
          
p =    0.078905684   [ANSWER, P VALUE]

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