Question

(05.01 MC)

Suppose we select a simple random sample of size n = 250 from a large population with a proportion p of successes. Let p̂ be the proportion of successes in the sample. For which value of p is it appropriate to use the Normal approximation for the sampling distribution of p̂? (4 points)

a	0.03
b	0.15
c	0.02
d	0.97
e	0.99

(05.04 MC)

A parks and recreational board in Birch County is interested in estimating the proportion of its residents in favor of having more public parks in that county. A random sample of Birch County residents was selected. All the selected residents were asked, "Are you in favor of having more public parks in your county?" A 98% confidence interval for the proportion of residents in favor of having more public parks in that county was calculated to be 0.54 ± 0.03. Which of the following statements is correct? (4 points)

a	At the 98% confidence level, the majority of area residents is in favor of having more public parks in that county.
b	At the 98% confidence level, the estimate of 0.54 is within 0.03 of the true proportion of county residents in favor of having more public parks in that county.
c	In repeated sampling, 98% of sample proportions will fall in the interval (0.51, 0.57).
d	In repeated sampling, the true proportion of county residents in favor of having more public parks in that county will fall in the interval (0.51, 0.57).
e	In repeated sampling, 98% of the time the true proportion of county residents in favor of having more public parks in that county will be equal to 0.54.

(05.05 MC)

The speed of a car, measured in miles per hour, was determined 10 times at random. The results are 22, 43, 35, 32, 41, 28, 29, 30, 37, and 43 miles per hour. Construct a 95% confidence interval for the mean speed of this vehicle. (4 points)

a	(28.9642, 39.0358)
b	(29.2226, 38.7774)
c	(28.9642, 38.7774)
d	(29.2226, 39.0358)
e	(29.9193, 38.0807)

Answer 1

1). the value of p is it appropriate to use the Normal approximation for the sampling distribution of p̂ is :-

0.02 (C)

[ explanation:-

n = 250.

we know that the conditions for normal approximation for the sampling distribution of p̂ is:-

]

4).the correct statement is:-

in repeated sampling, the true proportion of county residents in favor of having more public parks in that county will fall in the interval (0.51, 0.57). [D]

[ explanation:-

the 98% confidence interval is:-

]

5).95% confidence interval for the mean speed of this vehicle be:-

(28.9642, 39.0358) [ A]

[ explanation:-

steps in minitab:-

copy the data in a column of minitab and name it x stat basic statistics 1 sample t select one or more samples,each in a column,select x in the blank box optionsin confidence level type 95 ,in alternative hypothesis select mean hypothesized mean okok.

to round off your answer to 4 decimal places right click on the 95% CI for μ decimal places select 4

your output be:-

Descriptive Statistics

N	Mean	StDev	SE Mean	95% CI for μ
10	34.00	7.04	2.23	(28.9642, 39.0358)

μ: mean of x ]

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