Question

Jackson sampled 101 students and calculated an average of 6.5 hours of sleep each night with a standard deviation of 2.14. using a 95% confidence level, he also found that t* = 1.984. confidence space interval space equals space x with bar on top plus-or-minus t asterisk times space bevelled fraction numerator s over denominator square root of n end fraction a 95% confidence interval calculates that the average number of hours of sleep for working college students is between __________ hours. answer choices are rounded to the hundredths place.

a.) 6.08 and 6.92
b.) 6.46 and 6.92
c.) 6.15 and 6.94
d.) 6.46 and 6.54

Answer 1

Using the given sample mean, standard deviation, and t-value, the 95% confidence interval for the average number of hours of sleep for college students is between 6.08 hours and 6.92 hours.

Step-by-step explanation:

To calculate the 95% confidence interval for the average number of hours of sleep for college students, we use the formula:

Confidence Interval = ºr{x} ± t* × ( s / √ n )

Where:

ºr{x} = sample mean

t* = t-value corresponding to the desired level of confidence and degrees of freedom

s = sample standard deviation

n = sample size

Given values are:

ºr{x} = 6.5 hours

t* = 1.984

s = 2.14

n = 101

Inserting these values into the formula, we calculate the margin of error:

Margin of Error = 1.984 × (2.14 / √101) ≈ 1.984 × 0.213 ≈ 0.42

The 95% confidence interval is then:

6.5 ± 0.42

Lower limit = 6.5 - 0.42 = 6.08

Upper limit = 6.5 + 0.42 = 6.92

Therefore, the average number of hours of sleep for working college students is between 6.08 and 6.92 hours.