Question

A sports magazine reports that the mean number of hot dogs sold by hot dog vendors at a certain sporting event is equal to 150. A random sample of 50 hot dog vendors was selected, and the mean number of hot dogs sold by the vendors at the sporting event was 140. For samples of size 50, which of the following is true about the sampling distribution of the sample mean number of hot dogs sold by hot dog vendors at the sporting event?

A

For all random samples of 50 sporting events, the sample mean will be 150 hot dogs.

B

For all random samples of 50 hot dog vendors, the sample mean will be 140 hot dogs.

C

The mean of the sampling distribution of the sample mean is 150 hot dogs.

D

The mean of the sampling distribution of the sample mean is 140 hot dogs.

E

All random samples of 50 hot dog vendors will have a sample mean within 10 hot dogs of the population mean.

A certain company produces fidget spinners with ball bearings made of either plastic or metal. Under standard testing conditions, fidget spinners from this company with plastic bearings spin for an average of 2.7 minutes, while those from this company with metal bearings spin for an average of 4.2 minutes. A random sample of three fidget spinners with plastic bearings is selected from company stock, and each is spun one time under the same standard conditions; let x¯1 represent the average spinning time for these three spinners. A random sample of seven fidget spinners with metal bearings is selected from company stock, and each is likewise spun one time under standard conditions; let x¯2 represent the average spinning time for these seven spinners. What is the mean μ(x¯1−x¯2) of the sampling distribution of the difference in sample means x¯1−x¯2 ?

• 3(2.7)−7(4.2)=−21.3

  A

• 3−7=−4

  B

• 2.7−4.2=−1.5

  C

• 2.73−4.27=0.3

  D

• 4.2−2.7=1.5

E

A fair six-sided die will be rolled fifteen times, and the numbers that land face up will be recorded. Let x¯1x¯1 represent the average of the numbers that land face up for the first five rolls, and let x¯2x¯2 represent the average of the numbers landing face up for the remaining ten rolls. The mean μμ and variance σ2σ2 of a single roll are 3.5 and 2.92, respectively. What is the standard deviation σ(x¯1−x¯2)σ(x¯1−x¯2) of the sampling distribution of the difference in sample means x¯1−x¯2x¯1−x¯2?

• 2.92+2.922.92+2.92

  A

• 2.92−2.922.92−2.92

  B

• 2.925+2.9210−−−−−−−−√(2.925+2.9210

  C

• 2.9225+2.92210−−−−−−−−−−√2.9225+2.92210

  D

• 2.9225−2.92210−−−−−−−−−−√

• E

Answer 1

(1) In case of the sampling distribution of sample mean, the mean value is equal to the mean value of the underlying distribution. Hence, our mean here is 150 and the answer is - The mean of the sampling distribution of the sample mean is 150 hot dogs.

(2) The mean of the sampling distribution of the difference of the sample means will be equal to the difference in population. Here, our answer is: 2.7 - 4.2 = -1.5.

(3) The standard deviation of the sampling distribution of the difference in sample means will be: . Here, option C will be the correct answer.