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Chapter 9: Q. 98 (page 553)

Toastmasters International cites a report by Gallop Poll that 40% of Americans fear public speaking. A student believes that less than 40% of students at her school fear public speaking. She randomly surveys361 schoolmates and finds that135 report they fear public speaking. Conduct a hypothesis test to determine if the percent at her school is less than 40%.

Short Answer

Expert verified

They lack sufficient information to claim that less than 40%of pupils at her school are afraid of public speaking.

Step by step solution

01

Given information

Sample size, n=361

According to the report by Gallop Poll, the proportion of Americans who fear public speaking=40%

02

Explanation

The null hypothesis states that 40%of Americans fear public speaking and the alternative hypothesis states that less than 40%of Americans fear public speaking.

H0:p=0.40H0:p<0.40

The Z test statistic is:

z=p∧-pp1-pnp∧=xn=135361=0.374

z=p∧-pp1-pn=0.374-0.40p1-pn=-0.0260.0257=-1.01

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Most popular questions from this chapter

"The Problem with Angels," by Cyndy Dowling although this problem is wholly mine, the catalyst came from the magazine, Time. On the magazine cover I did find the realm of angels tickling my mind. Inside, 69%I found to be in angels, Americans do believe.

Then, it was time to rise to the task, ninety-five high school and college students I did ask. Viewing all as one group, random sampling to get the scoop. So, I asked each to be true, "Do you believe in angels?" Tell me, do! Hypothesizing at the start, totally believing in my heart that the proportion who said yes would be equal on this test. Lo and behold, seventy-three did arrive, out of the sample of ninety-five. Now your job has just begun, Solve this problem and have some fun.

The Weather Underground reported that the mean amount of summer rainfall for the northeastern US is at least 11.52 inches. Ten cities in the northeast are randomly selected and the mean rainfall amount is calculated to be 7.42 inches with a standard deviation of 1.3 inches. At the α = 0.05 level, can it be concluded that the mean rainfall was below the reported average? What if α = 0.01? Assume the amount of summer rainfall follows a normal distribution.

Some of the following statements refer to the null hypothesis, some to the alternate hypothesis. State the null hypothesis, H0, and the alternative hypothesis. Ha, in terms of the appropriate parameter (μorp).

a. The mean number of years Americans work before retiring is 34.

b. At most 60% of Americans vote in presidential elections.

c. The mean starting salary for San Jose State University graduates is at least \(100,000 per year.

d. Twenty-nine percent of high school seniors get drunk each month.

e. Fewer than 5% of adults ride the bus to work in Los Angeles.

f. The mean number of cars a person owns in her lifetime is not more than ten.

g. About half of Americans prefer to live away from cities, given the choice.

h. Europeans have a mean paid vacation each year of six weeks.

i. The chance of developing breast cancer is under 11% for women.

j. Private universities' mean tuition cost is more than \)20,000 per year.

Assume the null hypothesis states that the mean is at most 12. Is this a left-tailed, right-tailed, or two-tailed test?

Suppose that a recent article stated that the mean time spent in jail by a first-time convicted burglar is 2.5years. A study was then done to see if the meantime has increased in the new century. A random sample of 26first-time convicted burglars in a recent year was picked. The mean length of time in jail from the survey was 3years with a standard deviation of 1.8years. Suppose that it is somehow known that the population standard deviation is 1.5. If you were conducting a hypothesis test to determine if the mean length of jail time has increased, what would the null and alternative hypotheses be? The distribution of the population is normal.

a.Ho_______
b.Ha_______
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