# To identify:An important assumption for using the bootstrap method Question
Sampling distributions To identify:An important assumption for using the bootstrap method 2020-11-09
The sampling distribution of the sample median does not follow a normal distribution.
Thus, the correct option is (b).
The sample is a random sample from a population, which is not an important assumption.
Thus, option (a) is incorrect.
Option (c) is incorrect because there are outliers in the sample.
Conclusion:
An important assumption for using the bootstrap method is that the sample distribution for the sample median must not be well approximated by the normal distribution.

### Relevant Questions Identify which assumption is needed to use the linear regression model to make inferences about the relationship.
Identify which assumption is the least critical. Identify which assumption is needed to use the linear regression model to obtain a meaningful fit that represents the true relationship well. The Wall Street Journal reported that the age at first startup for $$55\%$$ of entrepreneurs was 29 years of age or less and the age at first startup for $$45\%$$ of entrepreneurs was 30 years of age or more.
a. Suppose a sample of 200 entrepreneurs will be taken to learn about the most important qualities of entrepreneurs. Show the sampling distribution of \overline{p} where \overline{p} is the sample proportion of entrepreneurs whose first startup was at 29 years of age or less.
b. Suppose a sample of 200 entrepreneurs will be taken to learn about the most important qualities of entrepreneurs. Show the sampling distribution of \overline{p} where \overline{p} is now the sample proportion of entrepreneurs whose first startup was at 30 years of age or more.
c. Are the standard errors of the sampling distributions different in parts (a) and (b)? After hearing of the national result that 44% of students engage in binge drinking (5 dri
a sitting for men, 4 for women), a professor surveyed a random sample of 244 students at his college and found that 96 of them admitted to binge drinking in the past week. Should he be surprised at this result? Explain. Which of the following statements about the sampling distribution of the sample mean is incorrect?
(a) The standard deviation of the sampling distribution will decrease as the sample size increases.
(b) The standard deviation of the sampling distribution is a measure of the variability of the sample mean among repeated samples.
(c) The sample mean is an unbiased estimator of the population mean.
(d) The sampling distribution shows how the sample mean will vary in repeated samples.
(e) The sampling distribution shows how the sample was distributed around the sample mean. The correct statement which is incorrect from the options about the sampling distribution of the sample mean
(a) the standard deviation of the sampling distribution will decrease as the sample size increases,
(b) the standard deviation of the sampling distribution is a measure of the variability of the sample mean among repeated samples,
(c) the sample mean is an unbiased estimator of the true population mean,
(d) the sampling distribution shows how the sample mean will vary in repeated samples,
(e) the sampling distributions shows how the sample was distributed around the sample mean. Explain the meaning of assertion that A is an unbiased estimator of $$\alpha$$ The distribution of height for a certain population of women is approximately normal with mean 65 inches and standard deviation 3.5 inches. Consider two different random samples taken from the population, one of size 5 and one of size 85.
Which of the following is true about the sampling distributions of the sample mean for the two sample sizes?
Both distributions are approximately normal with mean 65 and standard deviation 3.5.
A
Both distributions are approximately normal. The mean and standard deviation for size 5 are both less than the mean and standard deviation for size 85.
B
Both distributions are approximately normal with the same mean. The standard deviation for size 5 is greater than that for size 85.
C
Only the distribution for size 85 is approximately normal. Both distributions have mean 65 and standard deviation 3.5.
D
Only the distribution for size 85 is approximately normal. The mean and standard deviation for size 5 are both less than the mean and standard deviation for size 85.
E Critical Thinking Let x be a random variable representing the amount of sleep each adult in New York City got last night. Consider a sampling distribution of sample means $$\overline{x}$$.
How do the two $$\overline{x}$$ distributions for sample size $$n = 50\ and\ n = 100$$ compare? 