Question

9.3 Hmwk - Confidence Interval for Population Mean (Homework)

Given a variable that has a t distribution with the specified degrees of freedom, what percentage of the time will its value fall in the indicated region? (Round your answers to one decimal place.)
(a) 10 df, between -1.37 and 1.37

%

(b) 10 df, between -2.76 and 2.76

%

(c) 24 df, between -2.06 and 2.06

%

(d) 24 df, between -2.80 and 2.80

%

(e) 23 df, outside the interval from -2.81 to 2.81

%

(f) 24 df, to the right of 2.80

%

(g) 10 df, to the left of -1.81

%

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The authors of a paper describe an experiment to evaluate the effect of using a cell phone on reaction time. Subjects were asked to perform a simulated driving task while talking on a cell phone. While performing this task, occasional red and green lights flashed on the computer screen. If a green light flashed, subjects were to continue driving, but if a red light flashed, subjects were to brake as quickly as possible. The reaction time (in msec) was recorded. The following summary statistics are based on a graph that appeared in the paper.
n = 49   
x = 530
s = 65
(a)
Construct a 95% confidence interval for ?, the mean time to react to a red light while talking on a cell phone. (Round your answers to three decimal places.)

____, _____

c)
Suppose that the researchers wanted to estimate the mean reaction time to within 7 msec with 95% confidence. Using the sample standard deviation from the study described as a preliminary estimate of the standard deviation of reaction times, compute the required sample size. (Round your answer up to the nearest whole number.)
n =  

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The following are airborne times (in minutes) for 10 randomly selected flights from San Francisco to Washington Dulles airport.

270 257 268 285 274 275 266 258 271 281

(a)

Compute a 90% confidence interval for the mean airborne time for flights from San Francisco to Washington Dulles. (Round your answers to three decimal places.)

____, ____

Answer 1

Ans:

1)

df		t	p-value	percentage
10	two-tailed	1.37	0.201	20.1
10	two-tailed	2.76	0.020	2.0
24	two-tailed	2.06	0.050	5.0
24	two-tailed	2.8	0.010	1.0
23	two-tailed	2.81	0.010	1.0
24	one-tailed	2.8	0.005	0.5
10	one-tailed	1.81	0.050	5.0

2)Given that

n=49

df=49-1=48

critical t value=tinv(0.05,48)=2.011

a)95% confidence interval for mean

=530+/-1.96*(65/sqrt(49))

=530+/-18.670

=(511.330, 548.670)

c)z=1.96

Margin of error=7 m sec

Sample size required=(1.96*65/7)^2=331.24

3)From given data:

n=10

sample mean=270.5

sample standard deviation=8.935

df=10-1=9

critical t value=tinv(0.1,9)=1.833

90% confidence interval for the mean airborne time

=270.5+/-1.833*(8.935/sqrt(10))

=270.5+/-5.179

=(265.321, 275.679)