Question

A group of statistics students conducted a survey about smoking habits on campus to determine the proportion of students who believe that vaping is less harmful than smoking cigarettes. Of the 100 students surveyed, 75% think that smoking hookah is less harmful than smoking cigarettes. Since we don’t have an estimate for the population proportion (p), we will use when calculating the standard perror.a.Verify that the conditions are met to use a Normal Model. 4b. Create a 90% Confidence Interval. Show all your steps. c.Interpret the 90% Confidence Interval in the context of this problem. d.A national study found that 44% of U.S. adults think that vaping is less harmful than smoking cigarettes. Does this study at this campus indicate the views of the college students differ from the national opinion?

Answer 1

Solution:-

a) Yes all the conditions met.

The sample is random and independent.

The number of success and failure is greater than 5.

b) 90% Confidence Interval is C.I = (0.6788, 0.8212).

C.I = 0.75 + 1.645*0.0433
C.I = 0.75 + 0.07123
C.I = (0.6788, 0.8212)

c) If repeated samples were taken and the 90% confidence interval was computed for each sample, 90% of the intervals would contain the population proportion of 0.75.

d) Yes.

Since the confidence interval does not contains the proportion 0.44, hence this study at this campus indicate the views of the college students differ from the national opinion.