Exam 3: Descriptive Statistics: Numerical Methods

Quality control is an important issue at ACME Company,which manufactures light bulbs.To test the life hours of their light bulbs,they randomly sampled nine light bulbs and measured how many hours they lasted (mean = 346.6). 378,361,350,375,200,391,375,368,321 What is the variance?

In a study of the factors that affect success in economics,data were collected for 8 business students.Scores on a calculus placement test are given with economics final exam scores.The data are below. Calculus Placement Score Exam Final Score 17 73 21 66 11 64 16 61 15 70 11 71 24 90 27 68 It can be shown that for these data: $\bar{X}=17.75, \quad \bar{y}=70.38, \quad \sum_{i=1}^{8}\left(x_{i}-\bar{x}\right)^{2}=237.50$ $\sum_{i=1}^{8}\left(y_{i}-\bar{y}\right)^{2}=545.875, \quad \sum_{i=1}^{8}\left(x_{i}-\bar{x}\right)\left(y_{i}-\bar{y}\right)=140.75$ Calculate the sample correlation coefficient.

If the median of a data set is 760,the upper quartile is 950,and the lower quartile is 650,what is the interquartile range?

Find the z-score for an IQ test score of 142 when the mean is 100 and the standard deviation is 15.

The ending value of an initial investment can be calculated using weighted means.

An initial investment of $10,000 has a value of $7,382 at the end of year 1,a rate of return of 62.43 percent for year 2,and a geometric mean return at the end of year 3 of 0.512.Determine the rate of return for the third year.

Researchers wish to study fuel consumption rates based on speed.The data from 10 cars are below. Speed Miles/Gallon 15 14 23 17 30 20 35 24 42 26 45 23 50 18 54 15 60 11 65 10 It can be shown that for these data: $\bar{X}=41.9, \quad \bar{y}=17.8, \quad \sum_{i=1}^{10}\left(x_{i}-\bar{x}\right)^{2}=2352.9$ $\sum_{i=1}^{10}\left(y_{i}-\bar{y}\right)^{2}=267.6, \quad \sum_{i=1}^{10}\left(x_{i}-\bar{x}\right)\left(y_{i}-\bar{y}\right)=-270.2$ Calculate the sample correlation coefficient.

When calculating the geometric mean,a quantity of 1 is added to the n^th root of the product (1 + R_i),where i = 1,2,...n.

In a statistics class,the following 10 scores were randomly selected: 74,73,77,77,71,68,65,77,67,66. What is the median?

If there are 7 classes in a frequency distribution,then the fourth class will always contain the median.

A random sample of 60 students in the business statistics course answered a survey on the average number of hours they spent on statistics each week.Unfortunately,the original data were lost and all that remains is the frequency table below.From these data,calculate the estimated sample mean. Class Hrs 1 0-3 18 2 4-7 16 3 8-11 14 4 12-15 10 5 16-19 2

In the calculation of a mean for grouped data,we assume that the average of the measurements in each class equals the class midpoint.

In a statistics class,10 scores were randomly selected,with the following results: 74,73,77,77,71,68,65,77,67,66 What is the 90^th percentile?

Using Chebyshev's Theorem,approximate the minimum proportion of the data that will be within µ ± kσ for k = 3.2

In a hearing test,subjects estimate the loudness (in decibels)of a sound,and the results are: 68,67,70,71,68,75,68,62,80,73,68. What is the median?

According to a survey of the top 10 employers in a major city in the Midwest,a worker spends an average of 413 minutes a day on the job.Suppose the standard deviation is 26.8 minutes and the time spent is approximately a normal distribution. What are the times within which approximately 99.73 percent of all workers will fall?

The population mean is the average of the population measurements.

The Rivertown city council is attempting to choose one of four sites (A,B,C,or D)as the location for its new emergency facility.After the new emergency facility becomes available for service,the current emergency facility will be shut down.The project manager has estimated the following response times in minutes from each of the proposed sites to the four areas that must be served by the emergency facility. $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { Area Served }$ Proposed Site 1 2 3 4 A 5.2 4.4 3.6 6.5 B 6.0 7.4 3.4 4.0 C 5.8 5.9 5.9 5.8 D 4.3 4.8 6.5 5.1 The number of emergency runs from the current emergency facility to each of the four areas over the past year is as follows: Area 1 2 3 4 Number of runs 150 65 175 92 Compute the weighted mean response time from the proposed locations and determine which proposed site should be selected for the new emergency facility.

A correlation coefficient close to -1 says x and y are highly related.

The following table shows the Price-to-Earnings ratio for a stereo equipment manufacturing company between 1998 and 2002.The annual percentage growth rate of the P/E ratios is also calculated and given below. Year P/E Ratio Growth rate \% 1998 12.4 1999 14.6 17.74\%(1998-1999) 2000 11.1 -23.97\%(1999-2000) 2001 8.2 -26.13\%(2000-2001) 2002 6.8 -17.07\%(2001-2002) Calculate the geometric mean growth rate increase or decrease over the period from 1998 to 2002.