Question

Software instruction: A hybrid course is one that contains both online and classroom instruction. In a study performed at Middle Georgia State College, a software package was used as the main source of instruction in a hybrid college algebra course. The software tracked the number of hours it took for each student to meet the objectives of the course. In a sample of 44 students, the mean number of hours was 80.5, with a standard deviation of 51.4. Part: 0/2 Part 1 of 2 (a) Construct a 99.9% confidence interval for the mean number of hours it takes for a student to meet course objectives. Round the answers to one decimal place A 99.9% confidence interval for the mean number of hours it takes for a student to meet the course objectives is | | < μ< course objectives is

Answer 1

Solution :

Given that,

$\bar x$ = 80.5

s = 51.4

n = 44

Degrees of freedom = df = n - 1 = 44 - 1 = 43

At 99.9% confidence level the t is ,

$\alpha$ = 1 - 99.9% = 1 - 0.999 = 0.001

$\alpha$ / 2 = 0.001 / 2 = 0.0005

t_{$\alpha$ /2,df} = t_0.0005,43 = 3.532

Margin of error = E = t_{$\alpha$/2,df} * (s /$\sqrt$n)

= 3.532 * ( 51.4/ $\sqrt$44)

= 27.4

The 99.9% confidence interval estimate of the population mean is,

$\bar x$ - E < $\mu$ < $\bar x$ + E

80.5 - 27.4 < $\mu$ < 80.5 + 27.4

53.1 < $\mu$ < 107.9

(53.1,107.9)