Chapter 4 AP Stats Review

One concern about the depletion of the ozone layer is that the increase in ultraviolet (UV) light will decrease crop yields. An experiment was conducted in a green house where soybean plants were exposed to varying levels of UV, measured in Dobson units. At the end of the experiment the yield (kg) was measured. A regression analysis was performed with the following results: The least-squares regression line is the line that

• minimizes the sum of the distances between the actual UV values and the predicted UV values.

• minimizes the sum of the squared residuals between the actual yield and the predicted yield.

• minimizes the sum of the distances between the actual yield and the predicted UV.

• minimizes the sum of the squared residuals between the actual UV reading and the predicted UV values.

• minimizes the perpendicular distance between the regression line and each data point.

One concern about the depletion of the ozone layer is that the increase in ultraviolet (UV) light will decrease crop yields. An experiment was conducted in a green house where soybean plants were exposed to varying levels of UV, measured in Dobson units. At the end of the experiment the yield (kg) was measured. A regression analysis was performed with the following results: Which of the following is correct?

• If the UV value increases by 1 Dobson unit, the yield is expected to increase by 0.0463 kg.

• If the yield increases by 1 kg, the UV value is expected to decrease by 0.0463 Dobson units.

• If the UV value increases by 1 Dobson unit, the yield is expected to decrease by 0.0463 kg.

• The predicted yield is 4.3 kg when the UV value is 20 Dobson units.

• None of the above is correct.

All but one of the following statements contains an error. Which statement could be correct?

• There is a correlation of 0.54 between the position a football player plays and his weight.

• We found a correlation of r = –0.63 between gender and political party preference.

• The correlation between the distance travelled by a hiker and the time spent hiking is r = 0.9 meters per second.

• We found a high correlation between the height and age of children: r = 1.12.

• The correlation between mid-August soil moisture and the per-acre yield of tomatoes is r = 0.53.

The Gallup Poll interviews 1600 people. Of these, 18% say that they jog regularly. The news report adds: "The poll has a margin of error of plus or minus three percentage points at a 95% confidence level." You can safely conclude that

• 95% of all Gallup Poll samples like this one give answers within ±3% of the true population value.

• the percent of the population who jog is certainly between 15% and 21%.

• 95% of the population jog between 15% and 21% of the time.

• we can be 95% confident that the sample proportion is captured by the confidence interval.

• if Gallup took many samples, 95% of them would find that 18% of the people in the sample jog.

The weights (in pounds) of three adult males are 160, 215, and 195. The standard error of the mean of these three weights is

• 190

• 27.84

• 22.73

• 16.07

• 13.13

In preparing to construct a one-sample t interval for a population mean, suppose we are not sure if the population distribution is Normal. In which of the following circumstances would we not be safe constructing the interval based on an SRS for size 24 from the population?

• A stemplot of the data is roughly bell-shaped.

• A histogram of the data shows slight skewness.

• A stemplot of the data has a large outlier.

• The sample standard deviation is large.

• The t procedures are robust, so it is always safe.

Many television viewers express doubts about the validity of certain commercials. In an attempt to answer their critics, Timex Group USA wishes to estimate the proportion of consumers who believe what is shown in Timex television commercials. Let p represent the true proportion of consumers who believe what is shown in Timex television commercials. What is the smallest number of consumers that Timex can survey to guarantee a margin of error of 0.05 of less at a 99% confidence level?

• 550

• 600

• 650

• 700

• 750

You want to compute a 90% confidence interval for the mean of a population with unknown population standard deviation. The sample size is 30. The value of t^* you would use for this interval is

• 1.645

• 1.699

• 1.697

• 1.96

• 2.045

A radio talk show host with a large audience is interested in the proportion p of adults in his listening area who think the drinking ago should be lowered to 18. To find this out, he poses the following question to his listeners: "Do you think that the drinking age should be reduced to eighteen in light of the fact that 18-year-olds are eligible for military service?" He asks listeners to phone in and vote "Yes" if they agree the drinking age should be lowered and "No" if not. Of the 100 people who phoned in, 70 answered "Yes". Which of the following conditions for inference about a proportion using a confidence interval are violated?

• The data are a random sample from the population of interest.

• n is so large that both np̂ and n(1-p̂) are at least 10.

• The population is smaller than 10% of the population.

• #1 and #2

• #1, #2, and #3

A 90% confidence interval for the mean μ of a population is computed from a random sample and is found to be 9±3. Which of the following could be the 95% confidence interval based on the same data.

• 9 ± 1.96

• 9 ± 2

• 9 ± 3

• 9 ± 4

• Without knowing the sample size, any of the above answers could be the 95% confidence interval.