Statistics Challenge

What homework?

100

The p-value for a hypothesis test turns out to be 0.00708. At alpha= 2% level of significance, what is the proper decision?

 Do we reject Ho.

or

Do we do not Reject Ho. 

Do not reject Ho.

200

What calculator do we use in the following?

In 1998, as an advertising campaign, the Nabisco Company announced a "1000 Chips Challenge," claiming that every 18-ounce bag of their Chips Ahoy cookies contained at least 1000 chocolate chips. Dedicated statistics students at the Air Force Academy (no kidding) purchased some randomly selected bags of cookies and counted the chocolate chips. Some of their data are given below.

1219 1214 1087 1200 1419 1121 1325 1345 1244 

Find a 95% confidence interval for the mean number of chips in a bag of Chips Ahoy Cookies. 

Confidence interval for mean with data

300

Scores on a statistics final in a large class were normally distributed with a mean of 74 and a standard deviation of 6. Find the following probabilities, round to the fourth.What is the probability 6 randomly chosen scores had an average greater than 77.

0.1103

400

 A political candidate has asked you to conduct a poll to determine what percentage of people support her. If the candidate only wants a 0.5% margin of error at a 99% confidence level, what size of sample is needed? Give your answer in whole people.

66349

500

NO TECH: Grade Points Averages for a sample of 16 college freshmen were taken at a university. The distribution of GPAs is normal with the sample meaning of 3.1 and a sample standard deviation of 0.8. At this time, we know the average GPA for entering freshman is 2.7 nationwide, what is the probability of getting a sample mean 3.1 or larger?

0.2767

Test Me!

100

A school counselor heard that teenagers sleep an less than  9 hours per night on the weekend. The counselor wants to test if this figure holds true for students at their school, so they take a random sample of students and ask them about their weekend sleep habits.

What would be Ho and Ha?

Mu>=9 

Mu< 9

200

Suppose that alpha=0.05 and that the P-value is 0.0542.  Which of the following is the correct conclusion:

Reject Ho.

Do Not Reject Ho.

Reject Ha.

Accept Ho.

Do not Reject Ho.

300

Suppose the CEO claims that at least 80 percent of the company's 1,000,000 customers are very satisfied. We conduct a study in which 200 customers are surveyed using simple random sampling. The result: 140 out of 200 are very satisfied. Based on these results, is there enough evidence to support the claim? Assume a significance level of 0.05.

z=-3.54

P=0.0002

400

No TECH:

Abigail, reports that the average salary of assistant professors at 4-year colleges is more than than $70,000.  A sample of 1050 assistant professors has a mean salary of $72,500 and a standard deviation of $11,200.  At  test the researcher’s claim. 

5 steps:

Z=7.233

P=0.00

500

• DO NOT USE TECHNOLOGY: You believe that 90% of the COS students will graduate within 3 years.  Out of the 350 students 308 graduated within 3 years.  At, alpha=0.05 is this sufficient evidence to doubt your claim?   Round to 2 decimal places.

5 Steps:

z=-1.25

P=0.2123

Confidence to do anything!

100

• Hannah wanted to calculate a 95% confidence interval for the mean grade earned in, Introduction to Statistics. She takes a random sample of 20 students and calculates the sample mean and constructs a confidence interval.  However, she is unhappy with this confidence interval because the width is too wide. What are two things she can change to decrease the width?

Increase the sample size! or decrease the level of confidence!

200

Ernesto wanted to calculate the proportion of COS student that take Math 21 in their first semester. He is only willing to survey 200 students and will not survey anymore due to time constraints. What can he do to decrease the width of the confidence interval?

 Reduce the level of Confidence

300

Use Tech:  The data shown represents the age in years of doctors that are employed for Saint Agnes medical hospital.  Assume the population is approximately normal. Construct and interpret a 95% confidence interval for the mean age of doctors at Saint Agnes. Round to 2 decimal places and use a complete sentence.  50,35,42,36,48,39

(35.14, 48.19)

400

No Tech:

• A simple random sample of 200 individuals who are currently employed is asked if they work at home at least once per week. Of the 200 employed individual ssurveyed, 38 responded that they did work at home at least once per week. Construct a 95% confidence interval for the population proportion of employed individuals who work at home at least once per week. Round to 2 decimal places.

(0.13, 0.24)

500

• DO NOT USE TECHNOLOGY. In a random sample of 50 teachers it was determined that the mean length of of working was 12.5 years, with a standard deviation of 6.5 years. Construct and interpret a 99% confidence interval for the mean.  Round to 1 decimal place and use a complete sentence.

(10.04, 14.96)

What size?

100

What would happen to the width of the confidence interval if n got bigger?

Width gets smaller!

200

What is the assumed "P hat" for a sample size if "P hat" is not given!

p hat=0.5

300

USE TECHNOLOGY:  Joseph wishes to estimate the percentage of adults who support abolishing the penny. What size sample should be obtained if he wishes the estimate to be within 2.5% points with 99% confidence if the previous estimate is 0.36.

2654

400

NO TECH: A school administrator is concerned about the amount of credit card debt that college students have.  She wishes to conduct a poll to estimate the percentage of full-time college students who have credit card debt of $2000 or more.  How big of a sample will she need if she wants to be 95% confident and only have a margin of error of 3%?

1068

500

NO TECH:

In a random sample 136 of 400 people given a flu shot experienced some discomfort. Determine the minimum sample size needed if we wanted to be 95% confident and yet only have a margin of error of 2.5%?

1380