Question

1) Are unnecessary c-sections putting moms and babies health at risk? The procedure is a major surgery which increases risks for the baby (breathing problems and surgical injuries) and for the mother (infection, hemorrhaging, and risks to future pregnancies). According to the Center for disease control and prevention, about 32.2% of all babies born in the U.S. are born via c-section. The World Health Organization recommends that the US reduce this rate by 10%.

Some states have already been working towards this. Suspecting that certain states have lower rates than 32.2%, researchers randomly select 1200 babies from Wisconsin and find that 20.8% of the sampled babies were born via c-section.

Let p be the proportion of all babies in the U.S. that are born via c-section. Give the null and alternative hypotheses for this research question.

1) H₀: p = .322

H_a: p < .322

2) H₀: p = .322

H_a: p ≠ .322

3) H₀: p = .208

H_a: p ≠ .208

4) H₀: p < .322

H_a: p = .322

5) H₀: p = .322

H_a: p > .322

2) 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 15% 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 100 bags and finds that 31 of them are over-filled.

He plans to test the hypotheses: H₀: p = 0.15 versus H_a: p > 0.15 (where p is the true proportion of overfilled bags).

What is the test statistic?

1) 4.48

2) 3.46

3) -3.46

3) According to a Pew Research Center, in May 2011, 35% of all American adults had a smartphone (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 300 community college students at random and finds that 126 of them have a smartphone. In testing the hypotheses: H₀: p = 0.35 versus H_a: p > 0.35, she calculates the test statistic as Z = 2.54.

Use the Normal Table to help answer the p-value part of this question.

1) There is enough evidence to show that more than 35% of community college students own a smartphone (P-value = 0.0055).

2) There is not enough evidence to show that more than 35% of community college students own a smartphone (P-value = 0.9945).

3) There is not enough evidence to show that more than 35% of community college students own a smartphone (P-value = 0.011).

4) There is not enough evidence to show that more than 35% of community college students own a smartphone (P-value = 0.0055).

Answer 1

Solution:

Question 1)

Given: According to the Center for disease control and prevention, about 32.2% of all babies born in the U.S. are born via c-section. Thus p = 0.322

Claim: states have lower rates of all babies born in the U.S. born via c-section than 32.2%.

Give the null and alternative hypotheses for this research question.

Since claim is directional to left tail, this is left tailed test.

Thus correct answer is:

1) H₀: p = .322

H_a: p < .322

Question 2)

Given:

p = 0.15
x = Number of bags are that over-filled = 31
n = total bags = 100

Thus sample proportion is:

Hypotheses: H0: p = 0.15 versus Ha: p > 0.15
We have to find test statistic value:

Question 3)

Given:

p = proportion of all American adults had a smartphone

p = 0.35

H₀: p = 0.35 versus H_a: p > 0.35,

The test statistic value is: Z = 2.54.

Thus find p-value:

For right tailed test, p-value is given by:

p-value = P( Z > z test statistic)

p-value = P( Z > 2.54)

p-value =1 - P( Z < 2.54)

Look in z table for z = 2.5 and 0.04 and find corresponding area.

P( Z < 2.54) = 0.9945

Thus

p-value =1 - P( Z < 2.54)

p-value =1 - 0.9945

p-value = 0.0055

Decision Rule:
Reject H0, if P-value < 0.05 level of significance, otherwise we fail to reject H0

Since p-value = 0.0055 <   0.05 level of significance, we reject null hypothesis H0.

Thus correct answer is:

1) There is enough evidence to show that more than 35% of community college students own a smartphone (P-value = 0.0055).