Exam 6: Putting Statistics to Work

Provide an appropriate response. -For women at Durham College, times to run the 400 meters are normally distributed. Which of the following are the most plausible values for the mean and standard deviation?

State whether you would expect the data set to be normally distributed. -Scores on a test in which most students have near perfect scores and a few fail.

Provide an appropriate response. -Which quantity describes how widely data values are spread about the center of a distribution?

Provide an appropriate response. -Which of the following is not possible?

Solve the problem. -Frank's Furniture employees earned the following amounts last week: \ 542.27 \ 383.77 \ 172.37 \ 547.20 \ 200.49 \ 461.29 \ 261.33 \ 467.24 \ 205.97 What was the mean amount earned by an employee last week? Round your answer to the nearest cent.

Provide an appropriate response. -Traditionally in hypothesis testing the null hypothesis represents the "status quo" which will be overturned only if there is evidence against it. Which of the statements below might represent a Null hypothesis?

For the given data value, find the standard score and the percentile. -A data value 2.5 standard deviations above the mean.

Find the mode(s)for the given sample data. - $20,44,46,44,49,44,49$

Solve the problem. -Scores on a test are approximately normally distributed with a mean of 70 and a standard deviation of 9. The teacher wants to give A's to the top 10% of students and B's to the next 23%. What is the Bottom cutoff for a B grade? Round your answer to the nearest whole number.

Use the range rule of thumb to approximate the standard deviation. - $496,598,503,528,565,601,576,543$

Provide an appropriate response. -What does it mean for an observed difference to be statistically significant at the 0.01 level?

Solve the problem. -Suppose that the mean salary in a particular profession is $45,000 with a standard deviation of $2,000. To what percentile does a salary of $48,000 correspond?

Solve the problem. -Last year, nine employees of an electronics company retired. Their ages at retirement are listed below. Find the mean retirement age. Round your answer to the nearest tenth. 57 64 59 $53 \quad 66 \quad 58$ 675154

Solve the problem. -The volumes of soda in quart soda bottles are normally distributed with a mean of 32.3 oz and a standard deviation of 1.2 oz. What percentage of bottles contain less than 32 oz of soda?

State whether you think the difference between what occurred and what you would expect by chance is statisticallysignificant. -In nine out of the last ten years, the stock market has gone up.

For the given data value, find the standard score and the percentile. -A data value $1.8$ standard deviations below the mean.

State which type of average, the mean, median, or mode, would be most appropriate in the situation described. Explainyour thinking. -A state governor is planning a tax cut. A researcher calculates the average amount that will be saved by residents of the state. Which average would best convey the amount that will be saved by most residents of the state?

For the given data value, find the standard score and the percentile. -A data value 0.9 standard deviations below the mean.

Find the range for the given data. -Fred, a local mechanic, gathered the following data regarding the price, in dollars, of an oil and filter change at twelve competing service stations. 32.95 24.95 26.95 28.75 18.90 28.50 30.95 22.95 24.95 26.95 29.75 28.00

A hypothesis test is to be performed. Describe the two possible outcomes of the test using the context of the givensituation. -In a clinical study of an arthritis medication, $28 \%$ of those taking the placebo reported improvement. The manufacturer of the medication claims that among those taking the medication, the proportion reporting improvement will be higher than this. The hypotheses are as follows: Null hypothesis: proportion reporting improvement $= 28 \%$ Alternative hypothesis: proportion reporting improvement $> 28 \%$