Problem 8 [10 Pts]

In February 2017, a polling firm did a large-

n

random survey of the American population to find the level

of support for President Trump. They concluded from the sample that the average support for Trump was

49% (.49) with a 95% confidence interval of [44%, 54%]. Assuming that the methodology used was correct,

which of the following is true of the random survey (determine which of the statements are TRUE)?

(a)

The sampling distribution of the sample mean is normally distributed.

(b)

The standard deviation of the sampling distribution of the mean (

n

) is around 2.6% (0.026).

(c)

If we drew random samples of the population many times, 95% of the time the true level of support

will be between 44% and 54%.

(d)

Trump definitely does not have the support of a majority of Americans.

(e)

Trump's true level of support is between 44% and 54% with a 0.95 probability.

Explain why EACH of the above statements is true or false.