12-4 to 12-6 Statistics Practice

Over 83,000 students recently applied for admissions to UC Berkeley. For all samples of applicants,   $\overline{x}$  =3.69
Under Scheme A, repeated samples of 200 showed a standard deviation of .07. Under scheme B, repeated samples of 2500 showed a standard deviation of .02. The variable of interest is the student’s high school grade point average (GPA), out of a maximum of 4.0

Label each graph with its correct scheme. Your answer should look like either A,B or B,A $\$  

 $\$  Over 83,000 students recently applied for admissions to UC Berkeley. For all samples of applicants,   $\overline{x}$  =3.69
Under Scheme A, repeated samples of 200 showed a standard deviation of .07. Under scheme B, repeated samples of 2500 showed a standard deviation of .02. The variable of interest is the student’s high school grade point average (GPA), out of a maximum of 4.0.  What is the margin of error for Scheme A?

 $\$  Over 83,000 students recently applied for admissions to UC Berkeley. For all samples of applicants,   $\overline{x}$   =3.69
Under Scheme A, repeated samples of 200 showed a standard deviation of .07. Under scheme B, repeated samples of 2500 showed a standard deviation of .02. The variable of interest is the student’s high school grade point average (GPA), out of a maximum of 4.0. What is the margin of error for Scheme B?

 $\$  Over 83,000 students recently applied for admissions to UC Berkeley. For all samples of applicants,  $\overline{x}$  =3.69
Under Scheme A, repeated samples of 200 showed a standard deviation of .07. Under scheme B, repeated samples of 2500 showed a standard deviation of .02. The variable of interest is the student’s high school grade point average (GPA), out of a maximum of 4.0.
Calculate a reasonable interval (middle 95%) for estimating the mean GPA of all applicants. SHOW YOUR WORK.          

                 Scheme A interval: answer should look like
(lowerbound,upperbound)

 $\$  Over 83,000 students recently applied for admissions to UC Berkeley. For all samples of applicants,  $\overline{x}$   =3.69
Under Scheme A, repeated samples of 200 showed a standard deviation of .07. Under scheme B, repeated samples of 2500 showed a standard deviation of .02. The variable of interest is the student’s high school grade point average (GPA), out of a maximum of 4.0.
Calculate a reasonable interval (middle 95%) for estimating the mean GPA of all applicants. SHOW YOUR WORK.          

                 Scheme B interval: answer should look like
(lowerbound,upperbound)

Generally speaking, as the sample size increases, the width of the interval ____________________

A group of students was trying to determine the proportion of candies in a bag that are blue. The company claims that 24% of candies in bags are blue. A simulation was run 100 times. with a sample size of 50, based on the premise that 24% of the candies are blue. The approximately normal results of the simulation are shown in the dot plot above.

The simulation results in a mean of 0.254 and a standard deviation of 0.060. Based on this simulation, what is a plausible interval containing the middle 95% of the data?

• (0.194,0.314)

• (0.134,0.374)

• (-0.448,0.568)

• (0.254,0.374)

A study conducted in 2004 in New York City found that 212 out of computations. 1334 participants had hypertension. Kim ran a simulation of 100 studies based on these data. The output of the simulation is shown in the diagram above. At a 95% confidence level, the proportion of New York City residents with hypertension and the margin of error are closest to

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 $\$  Suppose 2 sets of test scores have the same mean, but different standard deviations,  $\sigma_1$  and  $\sigma_2$  , with  $\sigma_2>\sigma_1.$  Which statement best describes the variability of these data sets?

• Data set one has the greater variability.

• Data set two has the greater variability.

• The variability will be the same for each data set.

• No conclusion can be made regarding the variability of either set.