Loading [MathJax]/jax/output/CommonHTML/jax.js

StatTutor Lesson - The Sample Proportion ˆp

true
Stat Tutor
true
true
You have completed 0 question sequences out of 25.
The sample proportion p-hat
Video Player is loading.
Current Time 0:00
Duration 0:00
Loaded: 0%
Stream Type LIVE
Remaining Time 0:00
 
1x
    • Chapters
    • descriptions off, selected

      Questions 1-2

      126

      Question 1.

      For what type of response variable do we compute proportion?

      A.
      B.

      Incorrect. We compute proportion when the response variable is categorical.
      Correct. We compute proportion when the response variable is categorical.
      Incorrect. Try again.
      2

      Questions 3-4

      232

      Question 3.

      What is the symbol for sample proportion?

      A.
      B.
      C.
      D.

      Incorrect. "ˆp" is the symbol for population proportion.
      Correct. "ˆp" is the symbol for population proportion.
      Incorrect. Try again.
      2

      Question 5

      252

      Question 5.

      Suppose a random sample of 300 students at a state university were asked whether they attended their university's last home football game. Thirteen percent said they had. Is "13%" a statistic or a parameter?

      A.
      B.

      Incorrect. Since 13% is the percent from a sample, it is a statistic, not a parameter.
      Correct. Since 13% is the percent from a sample, it is a statistic, not a parameter.
      Incorrect. Try again.
      2

      Question 6

      322

      Question 6.

      How does the sampling distribution of ˆp differ from the sampling distribution of ¯x?

      A.
      B.
      C.

      Incorrect. The sampling distribution of ˆp is the distribution of ˆp's from all possible samples whereas the sampling distribution of ¯x is the distribution of ¯x's from all possible samples. One further difference not given in the answers: The responses of the population from which we sample to get ˆp's are categorical whereas the responses of the population from which we sample to get ¯x's are quantitative. But the sampling distributions do not consist of categorical or quantitative data, but either ˆp's or ¯x's.
      Correct. The sampling distribution of ˆp is the distribution of ˆp's from all possible samples whereas the sampling distribution of ¯x is the distribution of ¯x's from all possible samples. One further difference not given in the answers: The responses of the population from which we sample to get ˆp's are categorical whereas the responses of the population from which we sample to get ¯x's are quantitative. But the sampling distributions do not consist of categorical or quantitative data, but either ˆp's or ¯x's.
      Incorrect. Try again.
      2

      Question 7

      385

      Question 7.

      For what do we examine a histogram representing the approximate sampling distribution of ˆp?

      A.
      B.
      C.

      Incorrect. Since we have a histogram of ˆp's, we note shape, center and spread.
      Correct. Since we have a histogram of ˆp's, we note shape, center and spread.
      Incorrect. Try again.
      2

      Question 8

      441

      Question 8.

      What is the response variable for this example and is it categorical or quantitative?

      A.
      B.
      C.
      D.

      Incorrect. For each voter we recorded whether he/she voted for Douglas. This response is categorical. Note: We needed a categorical response variable so that we could demonstrate concepts about proportion.
      Correct. For each voter we recorded whether he/she voted for Douglas. This response is categorical. Note: We needed a categorical response variable so that we could demonstrate concepts about proportion.
      Incorrect. Try again.
      2

      Question 9

      458

      Question 9.

      What is the parameter for this example?

      A.
      B.
      C.
      D.

      Incorrect. The parameter for this example is the proportion of all voters who voted for Douglas.
      Correct. The parameter for this example is the proportion of all voters who voted for Douglas.
      Incorrect. Try again.
      2

      Questions 10-11

      544

      Question 10.

      True or false: The center of the histogram is about 0.21.

      A.
      B.

      Incorrect. The balance point of the histogram is at about 0.21.
      Correct. The balance point of the histogram is at about 0.21.
      Incorrect. Try again.
      2

      Question 12

      643

      Question 12.

      True or false: The estimated sampling distribution of ˆp for samples of size 40 is closer to Normal than the estimated sampling distribution of ˆp for samples of size 400.

      A.
      B.

      Incorrect. The opposite is correct. The estimated sampling distribution of ˆp for samples of size 400 is much closer to Normal than the estimated sampling distribution of ˆp for samples of size 40.
      Correct. The opposite is correct. The estimated sampling distribution of ˆp for samples of size 400 is much closer to Normal than the estimated sampling distribution of ˆp for samples of size 40.
      Incorrect. Try again.
      2

      Questions 13-14

      705

      Question 13.

      Fill in the blank: As the sample size increases, the spread of the sampling distribution of ˆp ______________.

      A.
      B.
      C.

      Incorrect. As sample size increases, the spread of the sampling distribution of ˆp decreases.
      Correct. As sample size increases, the spread of the sampling distribution of ˆp decreases.
      Incorrect. Try again.
      2

      Question 15

      732

      Question 15.

      Fill in the blank: The proportion of voters for Lincoln is _____________ the proportion of voters for Douglas.

      A.
      B.

      Incorrect. The proportion of voters for Lincoln is closer to 0.5 than the proportion of voters for Douglas.
      Correct. The proportion of voters for Lincoln is closer to 0.5 than the proportion of voters for Douglas.
      Incorrect. Try again.
      2

      Question 16

      840

      Question 16.

      What is the shape of the estimated sampling distributions of ˆp for samples of size n = 40 and n = 400?

      A.
      B.
      C.

      Incorrect. The shape of the estimated sampling distributions of ˆp for samples of size n = 40 and n = 400.
      Correct. The shape of the estimated sampling distributions of ˆp for samples of size n = 40 and n = 400.
      Incorrect. Try again.
      2

      Question 17

      888

      Question 17.

      Fill in the blank: The value of p for Lincoln is _____________ the value of p for Douglas.

      A.
      B.

      Incorrect. The proportion of voters for Lincoln is closer to 0.5 than the proportion of voters for Douglas. This is the key to the differences between the sampling distributions.
      Correct. The proportion of voters for Lincoln is closer to 0.5 than the proportion of voters for Douglas. This is the key to the differences between the sampling distributions.
      Incorrect. Try again.
      2

      Question 18

      971

      Question 18.

      The value of p for Douglas is p = 0.21. What is the mean of the sampling distribution of ˆp created by taking repeated samples of size n = 100 and computing the proportion for Douglas?

      A.
      B.
      C.

      Incorrect. The mean of the sampling distribution of ˆp is p = 0.21.
      Correct. The mean of the sampling distribution of ˆp is p = 0.21.
      Incorrect. Try again.
      2

      Question 19

      1015

      Question 19.

      The value of p for Douglas is p = 0.21. What is the standard deviation of the sampling distribution of ˆp created by taking repeated samples of size n=100 and computing the proportion for Douglas?

      A.
      B.
      C.

      Incorrect. The standard deviation of the sampling distribution of ˆp is 0.21(10.21)100.
      Correct. The standard deviation of the sampling distribution of ˆp is 0.21(10.21)100.
      Incorrect. Try again.
      2

      Question 20

      1058

      Question 20.

      The value of p for Douglas is p = 0.21. What is the shape of the sampling distribution of ˆp created by taking repeated samples of size n = 100 and computing the proportion for Douglas?

      A.
      B.
      C.

      Incorrect. n = 100 is large enough to apply the Central Limit Theorem and say that the shape is approxiately Normal.
      Correct. n = 100 is large enough to apply the Central Limit Theorem and say that the shape is approxiately Normal.
      Incorrect. Try again.
      2

      Question 21

      1075

      Question 21.

      True or false: The standard deviations differ because p for Douglas is p = 0.21 and p for Lincoln is p = 0.40.

      A.
      B.

      Incorrect. Standard deviation for the sampling distribution of ˆp depends on the value of p.
      Correct. Standard deviation for the sampling distribution of ˆp depends on the value of p.
      Incorrect. Try again.
      2

      Question 22

      1132

      Question 22.

      True or false: The requirement for "n large" for applying the Central Limit Theorem depends on np and n(1 - p).

      A.
      B.

      Incorrect. This is a correct statement.
      Correct. This is a correct statement.
      Incorrect. Try again.
      2

      Question 23

      1231

      Question 23.

      In order to apply the Central Limit Theorem to the shape of the sampling distribution of ˆp, which of the following conditions must be met?

      A.
      B.

      Incorrect. "n large" for applying the Central Limit Theorem depends on both np and n(1 - p); both must be 10 or larger.
      Correct. "n large" for applying the Central Limit Theorem depends on both np and n(1 - p); both must be 10 or larger.
      Incorrect. Try again.
      2

      Questions 24-25

      1345

      Question 24.

      Why was the shape of the sampling distribution of ˆp created from samples of size 40 of those for Lincoln closer to Normal than the shape of the sampling distribution of ˆp created from samples of size 40 of those for Douglas?

      A.
      B.

      Incorrect. p for Lincoln at p = 0.40 is closer to 0.5 than p for Douglas at p = 0.21.
      Correct. p for Lincoln at p = 0.40 is closer to 0.5 than p for Douglas at p = 0.21.
      Incorrect. Try again.
      2

      Applet

      1379

      Question 26

      1383

      Question 26.

      True or false: The shape of the sampling distribution of ˆp gets closer to Normal as n increases.

      A.
      B.

      Incorrect. This is the essence of the Central Limit Theorem for proportion.
      Correct. This is the essence of the Central Limit Theorem for proportion.
      Incorrect. Try again.
      2

      Question 27

      1512

      Question 27.

      Why is the shape of the sampling distribution of ˆp approximately Normal?

      A.
      B.

      Incorrect. np and n(1 - p) must both be bigger than 10 for the sampling distribution of ˆp to be approximately Normal.
      Correct. np and n(1 - p) must both be bigger than 10 for the sampling distribution of ˆp to be approximately Normal.
      Incorrect. Try again.
      2

      Question 28

      1606

      Question 28.

      On the basis of this probability, can we reject H0: p = 0.5?

      A.
      B.

      Incorrect. The z-score of 6.00 is off the chart and the P-value is essentially zero. This is so small that we can reject H0.
      Correct. The z-score of 6.00 is off the chart and the P-value is essentially zero. This is so small that we can reject H0.
      Incorrect. Try again.
      2

      Question 29

      1756

      Question 29.

      Why doesn't the population from which we sample have a mean and a standard deviation?

      A.
      B.
      C.

      Incorrect. We compute proportions for categorical data; we have to have quantitative data in order to compute a mean and a standard deviation.
      Correct. We compute proportions for categorical data; we have to have quantitative data in order to compute a mean and a standard deviation.
      Incorrect. Try again.
      2

      Question 30

      1778

      Question 30.

      What type of graph is used for categorical data?

      A.
      B.
      C.
      D.

      Incorrect. A bar graph is used to display categorical data; a histogram, a boxplot and a stem and leaf plot can be used to display quantitative data.
      Correct. A bar graph is used to display categorical data; a histogram, a boxplot and a stem and leaf plot can be used to display quantitative data.
      Incorrect. Try again.
      2