Question

1) A quality control engineer at a potato chip company tests the bag filling machine by weighing bags of potato chips. Not every bag contains exactly the same weight. But if more than 12% of bags are over-filled then they stop production to fix the machine. They define over-filled to be more than 1 ounce above the weight on the package.

The engineer weighs 103 bags and finds that 32 of them are over-filled. He plans to test the hypotheses H0: p = 0.12 versus Ha: p > 0.12. What is the test statistic? Round answer 2 decimal places

2)Does secondhand smoke increase the risk of a low weight birth? A baby is “low birth weight” if it weighs less than 5.5 pounds at birth. According to the National Center of Health Statistics, about 7.8% of all babies born in the U.S. are categorized as low birth weight. Researchers randomly select 1200 babies whose mothers had extensive exposure to secondhand smoke during pregnancy. 10.4% of the sample are categorized as low birth weight.

Which of the following are the appropriate null and alternative hypotheses for this research question.

a) H0: p = 0.078; Ha: p ≠ 0.078

b) H0: p = 0.078; Ha: p > 0.078

c) H0: p = 0.104; Ha: p ≠ 0.104

d) H0: μ = 0.104; Ha: μ > 0.104

3) Short-term classes: Does taking a class in a short-term format (8 weeks instead of 16 weeks) increase a student’s likelihood of passing the course? For a particular course, the pass rate for the 16-week format is 59%. A team of faculty examine student data from 40 randomly selected accelerated classes and determine that the pass rate is 78%.

Which of the following are the appropriate null and alternative hypotheses for this research question?

a) H0: p = 0.59; Ha: p ≠ 0.59

b) H0: p = 0.59; Ha: p > 0.59

c) H0: p = 0.78; Ha: p ≠ 0.78

d) H0: p = 0.78; Ha: p > 0.59

4)According to a Pew Research Center study, in May 2011, 35% of all American adults had a smart phone (one which the user can use to read email and surf the Internet). A communications professor at a university believes this percentage is higher among community college students. She selects 315 community college students at random and finds that 115 of them have a smart phone. Then in testing the hypotheses:

H0: p = 0.35 versus

Ha: p > 0.35,

what is the test statistic?

z =  . (Please round your answer to two decimal places.)

5)According to a Pew Research Center study, in May 2011, 32% of all American adults had a smart phone (one which the user can use to read email and surf the Internet). A communications professor at a university believes this percentage is higher among community college students. She selects 351 community college students at random and finds that 130 of them have a smart phone. In testing the hypotheses:

H0: p = 0.32 versus

Ha: p > 0.32,

she calculates the test statistic as z = 2.0230.

Then the p‑value = .

(Please round your answer to four decimal places.)

6)According to the Pew Research Center, the proportion of the American population who use only a cellular telephone (no landline) is 37%. Jason claims that the proportion of young American adults who do not have a landline is greater than 37%. He conducts a survey with a sample of randomly selected young American adults and finds that 38% do not have landlines.

If we set up our null and alternative hypotheses as follows:

H0:p=0.37

Ha:p>0.37

and find that: "p-value"=0.418. Does this provide enough evidence to support Jason’s claim? Use an α=0.05 level of significance.

Choose the correct answer below.

a)Since the p-value < α, do not reject the null hypothesis.

b) Since the p-value > α, do not reject the null hypothesis.

c) Since the p-value < α, reject the null hypothesis.

d) Since the p-value > α, reject the null hypothesis.

Answer 1

1. Sample proportion p = X/n = 32/103 = 0.3107

P-Value: 0.0000 so we reject H0

Thus we conclude that population proporiton is greater than 12% i.e. P > 0.12

2. Correct answer: Option b) H0: p = 0.078; Ha: p > 0.078

3. Correct answer: Option b) H0: p = 0.59; Ha: p > 0.59

4. From the given data

P-Value: 0.2874 which is > 0.05 so we accept H0

Thus we conclude that the professor believe is wrong

5. P-Value: 0.0215

6. Given P-value = 0.418 which is > alpha 0.05 so we conlcude that the proportion of the American population who use only a cellular telephone (no landline) is 37%.

Correct answer; Option b) Since the p-value > α, do not reject the null hypothesis.