Statistics Review 3

Data Collection and Exploration

100

An independent polling agency was hired to track the preferences of registered voters in a district for an upcoming election. The polling agency divided the district into twenty regions and believes that the regions are similar to one another in their composition. The agency then randomly selected two of the regions and surveyed all registered voters in both regions. What sampling method was used?

Cluster sampling

200

The manager of a public swimming pool wants to compare the effectiveness of two laundry detergents, Detergent A and Detergent B, in cleaning the towels that are used daily. As each dirty towel is turned in, it is placed into the only washing machine on the premises. When the washing machine contains 20 towels, the manager flips a coin to determine whether Detergent A or Detergent B will be used for that load. The cleanliness of the load of towels is rated on a scale of 1 to 10 by a person who does not know which detergent was used. The manager continues this experiment for many days. What kind of experimental design was used?

Completely randomized design

300

There is a linear relationship between the number of chirps made by the striped ground cricket and the air temperature. A least squares fit of some data collected by a biologist gives the model

ŷ = 25.2 + 3.3x            9 < x < 25,

where x is the number of chirps per minute and ŷ is the estimated temperature in degrees Fahrenheit. What is the estimated increase in temperature that corresponds to an increase of 5 chirps per minute?

16.5 degrees Fahrenheit

400

A researcher collected data on the latitude, in degrees north of the equator, and the average low temperature, in degrees Fahrenheit, for a random sample of cities in Europe. The data were used to create the following equation for the least-squares regression line.

predicted average low temp = 65.5 - 0.70(latitude)

Interpret the slope of the line.

For each one degree north of the equator increase, the predicted average low temperature decreases on average by 0.70 degree Fahrenheit.

500

Windmills generate electricity by transferring energy from wind to a turbine. A study was conducted to examine the relationship between wind velocity in miles per hour (mph) and electricity production in amperes for one particular windmill. The following regression (with conditions checked) was generated:

How much more electricity would the windmill be expected to produce on a day when the wind velocity is 25 mph than on a day when the wind velocity is 15 mph?

2.40 amperes higher

Probability

100

The table below shows the political party registration by gender of all 500 registered voters in Franklin Township. Given that a randomly selected registered voter is a male, what is the probability that he is registered for Party Y?

0.24

200

A complex electronic device contains three components, A, B, and C. The probabilities of failure for each component in any one year are 0.01, 0.03, and 0.04, respectively. If any one component fails, the device will fail. If the components fail independently of one another, what is the probability that the device will not fail in one year?

0.922

300

Let the random variable X represent the number of telephone lines in use by the technical support center of a software manufacturer at noon each day. Calculate the expected value of X.

P(X=0) = 0.35; P(X=1) = 0.20; P(X=2) = 0.15

P(X=3) = 0.15; P(X=4) = 0.10; P(X=5) = 0.05

1.6

400

A charity fundraiser has a Spin the Pointer game as shown below:

A donation of $2 is required to play the game. For each $2 donation, a player spins the pointer once and receives the amount of money indicated in the sector where the pointer lands on the wheel. The spinner has an equal probability of landing in each of the 10 sectors. What is the expected value of the net contribution to the charity for one play of the game?

70 cents

500

The XYZ Office Supplies Company sells calculators in bulk at wholesale prices, as well as individually at retail prices. Next year's sales depend on market conditions, but executives use probability to find estimates of sales for the coming year. The following tables are estimates for next year's sales. What profit does XYZ Office Supplies Company expect to make for the next year if the profit from each calculator sold is $20 at wholesale and $30 at retail. 

$220,700

Distributions

100

A uniform distribution takes on values such that -3 < X < 5. What is the height of the uniform distribution?

1/8

200

The commuting time for a student to travel from home to a college campus is normally distributed with a mean of 30 minutes and a standard deviation of 5 minutes. If the student leaves home at 8:25 A.M., what is the probability that the student will arrive at the college campus later than 9 A.M.?

0.16

300

The distribution of the lifespan of a battery is approximately normal with mean 30 months and standard deviation 8 months. In how many months is it expected that 25 percent of the batteries will no longer work?

24.6 months

400

The distribution of the weights of loaves of bread from a certain bakery follows approximately a normal distribution. Based on a very large sample, it was found that 10 percent of the loaves weighed less than 15.34 ounces, and 20 percent of the loaves weighed more than 16.31 ounces. What are the mean and standard deviation of the distribution of the weights of the loaves of bread?

mean: 15.93

SD: 0.46

500

A local radio station plays 40 rock-and-roll songs during each 4-hour show. The program director at the station needs to know the total amount of airtime for the 40 songs so that time can also be programmed during the show for news and advertisements. The distribution of the lengths of rock-and-roll songs is roughly symmetric with a mean length of 3.9 minutes and a standard deviation of 1.1 minutes. Describe the sampling distribution of the sample mean song lengths for random samples of 40 rock-and-roll songs.

Approximately Normal

Mean: 3.9

Standard deviation: 1.1/sqrt(40) or 0.174

Inference for Proportions

100

A 90% Confidence Interval is generated for a 1-sample proportion. what is the minimum sample size needed for the margin of error to be within 0.02?

1692

200

A humane society wanted to estimate with 95 percent confidence the proportion of households in its county that own at least one dog. The resulting confidence interval was 0.417 +/- 0.119. A national pet products association claimed that 39% of all American households owned at least one dog. Does the humane society’s interval estimate provide evidence that the proportion of dog owners in its county is different from the claimed national proportion? Explain.

No, because 0.39 is within the confidence interval.

300

A survey was conducted to determine what percentage of college seniors would have chosen to attend a different college if they had known then what they know now. In a random sample of 100 seniors, 34 percent indicated that they would have attended a different college. A 90 percent confidence interval for the percentage of all seniors who would have attended a different college is

26.2% to 41.8%

400

In 2011, 17% of a random sample of 200 adults in the US indicated that they consumed at least 3 pounds of bacon that year. In 2016, 25% of a random sample of 600 adults in the US indicated that they consumed at least 3 pounds of bacon that year.

Assuming all conditions for inference are met, what is the most appropriate test statistic formula to use to investigate whether the proportion of all adults in the US who consume at least 3 pounds of bacon in 2016 is different from that of 2011?

500

A polling agency is interested in whether voter support has increased following the recent debate. A hypothesis test is conducted with an alpha level of 0.08. If a confidence interval were constructed instead, what would be an equivalent level of confidence?

0.84 or 84%

Inference for Means

100

An automobile manufacturer claims that the average gas mileage of a new model is 35 miles per gallon (mpg). A consumer group is skeptical of this claim and thinks the manufacturer may be overstating the average gas mileage. What is the null and alternative hypotheses that the consumer group should test?

H0: µ = 35 mpg

Ha: µ < 35 mpg

200

A confidence interval for 1-sample means is found to be (14.90, 17.40). What is the point estimate?

16.15

300

A 85% confidence interval for 1-sample means is found to be (14.90, 16.60). The sample size is over 1000. What is the approximate standard error of the sampling distribution?

0.59

400

When a virus is placed on a banana leaf, small lesions appear on the leaf. To compare the mean number of lesions produced by two different strains of virus, one strain is applied to half of each of 8 banana leaves, and the other strain is applied to the other half of each leaf. The strain that goes on the right half of the leaf is decided by a coin flip. The lesions that appear on each half are then counted. What is an appropriate test?

paired t-test

500

It is claimed that the average amount of active ingredient per pain-reliever tablet is at least 200 milligrams. The Consumer Watchdog Bureau tests a random sample of 70 tablets. The mean content of the active ingredient for this sample is 194.3 milligrams, with a standard deviation of 21 milligrams. What is the approximate p-value for the appropriate test?

0.013