# answer the question 94

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1. Some of the statements below refer to the null hypothesis, some to the alternate hypothesis.

State the null hypothesis, *H*_{0}, and the alternative hypothesis, *H*_{a}, in terms of the appropriate parameter (*Î¼* or *p*).

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

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

-The mean starting salary for San Jose State University graduates is at least $100,000 per year.

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

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

– The mean number of cars a person owns in her lifetime is not more than 10.

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

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

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

– Private universities’ mean tuition cost is more than $20,000 per year.

( answer those like this format example :*H*_{0}: *p* â‰¥ 20,000, *H*_{a}: *p* < 20,000)

2. When a new drug is created, the pharmaceutical company must subject it to testing before receiving the necessary permission from the Food and Drug Administration (FDA) to market the drug. Suppose the null hypothesis is “the drug is unsafe.” What is the Type II Error?

3. A statistics instructor believes that fewer than 20% of Evergreen Valley College (EVC) students attended the opening midnight showing of the latest Harry Potter movie. She surveys 84 of her students and finds that 11 attended the midnight showing. The Type I error is to conclude that the percent of EVC students who attended is ________.

4.It is believed that Lake Tahoe Community College (LTCC) Intermediate Algebra students get more than 7 hours of sleep per night, on average. A survey of 22 LTCC Intermediate Algebra students generated a mean of 7.24 hours with a standard deviation of 1.93 hours. At a level of significance of 5%, do LTCC Intermediate Algebra students get less than 7 hours of sleep per night, on average?The Type II error is not to reject that the mean number of hours of sleep LTCC students get per night is at most seven when, in fact, the mean number of hours is 7 hours.

5. From generation to generation, the mean age when smokers first start to smoke varies. However, the standard deviation of that age remains constant at around 2.1 years. A survey of 35 smokers of this generation was done to see if the mean starting age is at least 19. The sample mean was 18.2 with a sample standard deviation of 1.3. Do the data support the claim at the 5% level?

Note: If you are using a Student’s *t*-distribution for the problem, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)

State the null hypothesis.

State the alternative hypothesis.

In words, state what your random variable *X-* represents.

State the distribution to use for the test. (Round your answers to four decimal places.)

*X- ~*

*What is the test statistic? (If using the z distribution round your answers to two decimal places, and if using the t distribution round your answers to three decimal places.) *

*What is the p-value? (Round your answer to four decimal places.) *

*Indicate the correct decision (“reject” or “do not reject” the null hypothesis), the reason for it, and write an appropriate conclusion.(i) Alpha (Enter an exact number as an integer, fraction, or decimal.) *

Construct a 95% confidence interval for the true mean. Sketch the graph of the situation. Label the point estimate and the lower and upper bounds of the confidence interval. (Round your lower and upper bounds to two decimal places.)

6. The mean number of sick days an employee takes per year is believed to be about 10. Members of a personnel department do not believe this figure. They randomly survey 8 employees. The number of sick days they took for the past year are as follows: 11; 6; 13; 4; 10; 8; 8; 8. Let *X* = the number of sick days they took for the past year. Should the personnel team believe that the mean number is about 10? Conduct a hypothesis test at the 5% level.

Note: If you are using a Student’s *t*-distribution for the problem, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)

State the null hypothesis.

State the alternative hypothesis.

State the distribution to use for the test. (Enter your answer in the form *z* or *t*_{df} where *df* is the degrees of freedom.)

What is the test statistic? (If using the *z* distribution round your answers to two decimal places, and if using the *t* distribution round your answers to three decimal places.)

What is the *p*-value? (Round your answer to four decimal places.)

Indicate the correct decision (“reject” or “do not reject” the null hypothesis), the reason for it, and write an appropriate conclusion.

(i) Alpha (Enter an exact number as an integer, fraction, or decimal.)*Î±* =

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

7. 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 that less than thirty percent of the teen girls smoke to stay thin?

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

Do not reject *H*_{0}: There is not sufficient evidence to conclude that less than 30% of teen girls smoke to stay thin.

Do not reject *H*_{0}: There is not sufficient evidence to conclude that more than 30% of teen girls smoke to stay thin.

Reject *H*_{0}: There is sufficient evidence to conclude that less than 30% of teen girls smoke to stay thin.

Reject *H*_{0}: There is sufficient evidence to conclude that more than 30% of teen girls smoke to stay thin.

Do not reject *H*_{0}: There is sufficient evidence to conclude that more than 30% of teen girls smoke to stay thin.

8. 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, 32 of 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’s *t*-distribution for the problem, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)

State the distribution to use for the test. (Round your standard deviation to four decimal places.)

What is the test statistic? (Round your answer to two decimal places.)

What is the *p*-value? (Round your answer to four decimal places.)

Indicate the correct decision (“reject” or “do not reject” the null hypothesis), the reason for it, and write an appropriate conclusion.

(i) Alpha:*Î±* =

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.)

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