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SAMPLING DISTRIBUTIONS CHECKPOINT 2
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The length of human pregnancy is known to have mean length of 268 days. A random sample of 64 pregnant women was selected and it was found that the average pregnancy length in that sample was 266 days.
Which of the following is a true statement about this scenario?
268 is a parameter and 266 is a statistic
Which, if any, of the following statements about the sampling distribution of the sample mean, x-bar, are false?
None of the above are false
All the statements are correct. (A) the sampling distribution of x-bar becomes closer and closer to normal as the sample size, n, increases. This happens regardless of the distribution of the variable in the population. The only thing that will be affected by the population distribution is how large the sample size n should be to get normality. (B) if the population distribution happens to be normal to start with, then the sampling distribution of x-bar is always normal, regardless of the sample size. (C) the sampling distribution of x-bar has mean μ, the same as the population mean. (D) the sampling distribution of x-bar has standard deviation σn√/, which is smaller than the population standard deviation. which is σ.
To estimate the mean number of daily study hours in the population of all the students at a large public university, a researcher plans to randomly sample students from this population and then calculate the average number of daily study hours for the sample (x-bar). Pictured below (in scrambled order) are three histograms:
The distribution of study hours in the population of all students in the university
The sampling distribution x-bar when samples of size n=5 are chosen from the population.
The sampling distribution x-bar when samples of size n=30 are chosen from the population.
Which of the following 6 possible orderings of the three histograms represents the sequence:
Population distribution
Sampling distribution of x-bar for sample size n = 5
Sampling distribution of x-bar for sample size n = 30?
histogram 2, histogram 3, histogram 1
To estimate the mean number of daily study hours in the population of all the students at a large public university, a researcher plans to randomly sample students from this population and then calculate the average number of daily study hours for the sample (x-bar). Pictured below (in scrambled order) are three histograms:
The distribution of study hours in the population of all students in the university
The sampling distribution x-bar when samples of size n=5 are chosen from the population.
The sampling distribution x-bar when samples of size n=30 are chosen from the population.
Based on the histograms, the most likely value of the population mean is:
3.0
Suppose that a candy company makes a candy bar whose weight is supposed to be 50 grams, but in fact, the weight varies from bar to bar according to a normal distribution with mean μ = 50 grams and standard deviation σ = 2 grams.
If the company sells the candy bars in packs of 4 bars, what can we say about the likelihood that the average weight of the bars in a randomly selected pack is 4 or more grams lighter than advertised?
It is extremely unlikely for this to occur; the probability is very close to 0
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