Prob and Stats Chapter 6 Review

These symbols represent the mean and standard deviation for which of the following distributions?

• The Population
• The Sample
• The Sampling Distribution

These symbols represent the mean and standard deviation for which of the following distributions?

• The Population
• The Sample
• The Sampling Distribution

A study of voting chose 663 registered voters at random shortly after an election. Of these, 72% said they had voted in the election. Election records show that only 56% of registered voters voted in the election. Which of the following statements is true about these percentages?

• 72% and 56% are both statistics

• 72% is a statistic and 56% is a parameter

• 72% is a parameter and 56% is a statistic

• 72% and 56% are both parameters

A state trooper randomly selects 50 cars driving on the freeway, records the state identified on the license plate, and calculates the proportion of cars with out-of-state plates. Which of the following describes the sampling distribution of the sample proportion in this context?

• The distribution of state for all cars in the troopers sample of cars on the freeway

• The distribution of state for all cars passing on this freeway

• The distribution of the proportion of cars with out-of-state plates in all possible samples of 50 cars on this freeway

• The distribution of the proportion of cars with out-of-state plates in the trooper's sample of 50 cars on this freeway

At a high school, 85% of students are right-handed. Let X = the number of students who are right-handed in a random sample of 10 students from the school. Which of the following statements about the mean and standard deviation of the sampling distribution of X is true?

• $\mu=8.5;\ \sigma_x=1.129$

• $\mu=8.5;\ \sigma_x=0.113$

• $\mu=8.5;\ \sigma_x\ \approx$ cannot be determined from the information given

• Neither the mean or the standard deviation can be determined from the information given

The student newspaper at a large university asks an SRS of 250 undergraduates, "Do you favor eliminating the carnival from the end-of-term celebration?" In this sample, 150 of the 250 undergraduates are in favor. Suppose that 55% of all undergraduates favor eliminating the carnival. If you took a very large number of SRSs of size n = 250 from this population, the sampling distribution of the sample proportion would have which of the following characteristics?

• Mean = 0.55; standard deviation = 0.03; shape unknown

• Mean = 0.55; standard deviation = 0.03; shape approximately Normal

• Mean = 0.60; standard deviation = 0.03; shape unknown

• Mean = 0.60; standard deviation = 0.03; shape approximately Normal

 Scores on the SAT math exam followed a normal distribution with mean 515 and standard deviation 114. You choose a SRS of 100 students and calculate a mean math score. Which of the following are the mean and standard deviation of the sampling distribution of the sample means?

• Mean = 515; SD = 114

• Mean = 515; SD =  $\frac{114}{\sqrt{100}}$  

• Mean =  $\frac{515}{100}$  ; SD =  $\frac{114}{100}$  

• Mean =  $\frac{515}{100}$  ; SD =  $\frac{114}{\sqrt{100}}$  

In a congressional district, 55% of the registered voters are Democrats. Which of the following is closest to the probability of getting less than 50% Democrats in a random sample of size 100?

• 0.157

• 0.496

• 0.504

• 0.843

The central limit theorem is important in statistics because it allows us to use the normal distribution to find probabilities involving the sample mean if the

• sample size is reasonably large for any population shape

• sample size is reasonably large AND the population is normally distributed

• population size is reasonably large for any population shape

• population size is reasonably large and the population is normally distributed.

Below is the population distribution of midterm scores for students in an introductory statistics class. The true mean of the population is  $\mu=76$   and the standard deviation is  $\sigma=8$ .  Is the shape of the sampling distribution of sample means approximately normal? Justify.

• Yes, because of Large Counts.

• Yes, because the population is more than 30.

• No, because the population is not symmetric and the sample size is more than 30.

• No, because the population is not symmetric and the sample size is NOT more than 30.