Question 1 multiple choice

Over the past few decades, public health officials have examined the link between weight concerns and teen girls' smoking. Researchers surveyed a group of 273 randomly selected teen girls living in Massachusetts (between 12 and 15 years old). After four years the girls were surveyed again. Sixty-three said they smoked to stay thin. Is there good evidence thatmore thanthirty percent of the teen girls smoke to stay thin?

After conducting the test, what are your decision and conclusion?

a) RejectH₀: There is sufficient evidence to conclude that more than 30% of teen girls smoke to stay thin.

b) Do not rejectH₀: There is not sufficient evidence to conclude that more than 30% of teen girls smoke to stay thin.

c) Do not rejectH₀: There is not sufficient evidence to conclude that less than 30% of teen girls smoke to stay thin.

d) RejectH₀: There is sufficient evidence to conclude that less than 30% of teen girls smoke to stay thin.

e) Do not rejectH₀: There is sufficient evidence to conclude that more than 30% of teen girls smoke to stay thin.

f) RejectH₀: There is not sufficient evidence to conclude that more than 30% of teen girls smoke to stay thin.

Question 2

In a particular year, 68% of online courses taught at a system of community colleges were taught by full-time faculty. To test if 68% also represents a particular state's percent for full-time faculty teaching the online classes, a particular community college from that state was randomly selected for comparison. In that same year,35of the 44 online courses at this particular community college were taught by full-time faculty. Conduct a hypothesis test at the 5% level to determine if 68% represents the state in question.

Note: If you are using a Student'st-distribution for the problem, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)

• Part (a) Multiple choice
• State the null hypothesis.

a) H₀:p0.68

b) H₀:p0.68

c) H₀:p= 0.68

d) H₀:p0.68

• Part (b) Multiple choice
• State the alternative hypothesis.

a) H_a:p= 0.68

b) H_a:p0.68

c) H_a:p<0.68

d) H_a:p>0.68

• Part (c) multiple choice
• In words, state what your random variableP'represents.

a) P'represents the proportion of the state's online classes taught by full-time faculty.

b) P'represents the proportion of all faculty members that teach the state's online classes.

c) P'represents the average number of the state's online classes taught by full-time faculty.

d) P'represents the number of the state's online classes taught by full-time faculty.

• Part (d)
• State the distribution to use for the test. (Round your standard deviation to four decimal places.)
• P'~______(______,______)
• Part (e)
• What is the test statistic? (Round your answer to two decimal places.)
• (t or z) = ______
• Part (f)
• What is thep-value? (Round your answer to four decimal places.)
• Explain what thep-value means for this problem.

a) IfH₀is false, then there is a chance equal to thep-value that the proportion of online courses taught by full-time faculty is at least as different as the sample proportion is from 68%.

b) IfH₀is true, then there is a chance equal to thep-value that the proportion of online courses taught by full-time faculty is not at least as different as the sample proportion is from 68%.

c) IfH₀is true, then there is a chance equal to thep-value that the proportion of online courses taught by full-time faculty is at least as different as the sample proportion is from 68%.

d) IfH₀is false, then there is a chance equal to thep-value that the proportion of online courses taught by full-time faculty is not at least as different as the sample proportion is from 68%.

• Part (g)
• Sketch a picture of this situation. Label and scale the horizontal axis and shade the region(s) corresponding to thep-value. (Upload your file below.)
• Part (h)
• Indicate the correct decision ("reject" or "do not reject" the null hypothesis), the reason for it, and write an appropriate conclusion.
• (i) Alpha:
• =________
• (ii) Decision:

a) reject the null hypothesis

b) do not reject the null hypothesis

• (iii) Reason for decision:

a) Since<p-value, we reject the null hypothesis.

b) Since>p-value, we reject the null hypothesis.

c) Since<p-value, we do not reject the null hypothesis.

d) Since>p-value, we do not reject the null hypothesis.

• (iv) Conclusion:

a) There is sufficient evidence to conclude that the percent of online courses taught at community colleges in the state is not equal to 68%.

b) There is not sufficient evidence to conclude that the percent of online courses taught at community colleges in the state is not equal to 68%.

• Part (i)
• Construct a 95% confidence interval for the true proportion. Sketch the graph of the situation. Label the point estimate and the lower and upper bounds of the confidence interval. (Round your answers to four decimal places.)