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Interpret confidence intervals for population means

A pharmaceutical company has developed a new drug to reduce cholesterol. A regulatory agency will recommend the new drug for use if there is convincing evidence that the mean reduction in cholesterol level after one month of use is more than

20\,\text{mg/dl}

, because a mean reduction of this magnitude would be greater than the mean reduction for the current most widely used drug. The pharmaceutical company collected data by giving the new drug to a random sample of

50

people from the population of people with high cholesterol. The reduction in cholesterol level after one month of use was recorded for each individual in the sample, resulting in a sample mean of

\bar{x}=24\,\text{mg/dl}

and a standard deviation of

s_{x}=15\,\text{mg/dl}

. Perform a significance test at a

5\%

significance level.

Malik walked up and back down an empty

18 \mathrm{~m}

long escalator at a constant rate. Since the escalator was going up at the time, it took him only

22.5 \mathrm{~s}

. Going down took Malik

90

s. Assume the escalator speed is constant.

\newline

What was Malik's walking speed?

\newline

\frac{\mathrm{m}}{\mathrm{s}}

A random sample of international flights in

2013

79 \%

of the flights arrived within

15

minutes of their scheduled arrival time, and this estimate had a margin of error of

3 \%

95 \%

confidence level. Which of the following conclusions is best?

\newline

1

\newline

79 \%

15

minutes of their scheduled times.

\newline

76 \%

15

minutes of their scheduled times.

\newline

76 \%

82 \%

15

minutes of their scheduled times.

\newline

92 \%

98 \%

15

minutes of their scheduled times.

Based on random samples of river heights, oceanographers estimate that

4

800

cubic kilometers

\left(\mathrm{km}^{3}\right)

of freshwater is discharged into the Arctic Ocean annually. The estimate has a margin of error of

240 \mathrm{~km}^{3}

90 \%

confidence level. Which of the following is the most reasonable claim about the volume of freshwater discharged annually into the Arctic Ocean?

\newline

1

\newline

A) It is between

4

800

5,040 \mathrm{~km}^{3}

\newline

B) It is between

4

560

5,040 \mathrm{~km}^{3}

\newline

(C) It is between

240

4,800 \mathrm{~km}^{3}

\newline

(D) It is between

240

4,320 \mathrm{~km}^{3}

1

578

randomly selected American adults,

44.8 \%

of the respondents said that airlines should allow in-flight calls on airplanes. The poll reported a margin of error of

2.5 \%

95 \%

confidence level. Which of the following is most likely to be equal to the percentage of all American adults who would say that airlines should allow in-flight calls?

\newline

1

\newline

40 \%

\newline

43 \%

\newline

48 \%

\newline

95 \%

A random sample of

35

four-door passenger vehicles had a mean gas mileage, in miles per gallon

(\mathrm{mpg})

25.9 \mathrm{mpg}

. The estimate had a margin of error of

2.6 \mathrm{mpg}

98 \%

confidence level. Of the following, which is the most plausible value for the true mean gas mileage of all four-door passenger vehicles?

\newline

1

\newline

24 \mathrm{mpg}

\newline

29 \mathrm{mpg}

\newline

32 \mathrm{mpg}

\newline

35 \mathrm{mpg}