Mathematics, 31.07.2020 02:01 gadgetady5699

The Department of Education would like to test the hypothesis that the average debt load of graduating students with a bachelor's degree is equal to $17,600. A random sample of 28 students had an average debt load of $18,800. It is believed that the population standard deviation for student debt load is $4800. The α is set to 0.05. The confidence interval for this hypothesis test would be .

Answers: 2

Show answers

Answers

A 95% confidence interval for the population average debt load of graduating students with a bachelor's degree is [$17,022.05, $20,577.94].

Step-by-step explanation:

We are given that a random sample of 28 students had an average debt load of $18,800. It is believed that the population standard deviation for student debt load is $4800. The α is set to 0.05.

Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;

P.Q. = $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\bar X$ = sample average debt load = $18,800

$\sigma$ = population standard deviation = $4,800

n = sample of students = 28

$\mu$ = population average debt load

Here for constructing a 95% confidence interval we have used a One-sample z-test statistics because we know about population standard deviation.

So, 95% confidence interval for the population mean, $\mu$ is ;

P(-1.96 < N(0,1) < 1.96) = 0.95 {As the critical value of z at 5% level of

significance are -1.96 & 1.96}

P(-1.96 < $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ < 1.96) = 0.95

P( $-1.96 \times {\frac{\sigma}{\sqrt{n} } }$ < ${\bar X-\mu}$ < $1.96 \times {\frac{\sigma}{\sqrt{n} } }$ ) = 0.95

P( $\bar X-1.96 \times {\frac{\sigma}{\sqrt{n} } }$ < $\mu$ < $\bar X+1.96 \times {\frac{\sigma}{\sqrt{n} } }$ ) = 0.95

95% confidence interval for $\mu$ = [ $\bar X-1.96 \times {\frac{\sigma}{\sqrt{n} } }$ , $\bar X+1.96 \times {\frac{\sigma}{\sqrt{n} } }$ ]

= [ $\$18,800-1.96 \times {\frac{\$4,800}{\sqrt{28} } }$ , $\$18,800+1.96 \times {\frac{\$4,800}{\sqrt{28} } }$ ]

= [$17,022.05, $20,577.94]

Therefore, a 95% confidence interval for the population average debt load of graduating students with a bachelor's degree is [$17,022.05, $20,577.94].

Answer from: Quest

x=17

step-by-step explanation:

solve 3x-24=x+10

then that makes it 2x=34 because you subtract an x from both sides to get rid of the one on the right, and then you add 24 to both sides to get rid of the 24 on the left

divide by both sides by 2 to get your answer so that you can get your answer

In circle a, bae dae. what is the value of x?

Answer from: Quest

answerthe vertex form

step-by-step explanation:

Another question on Mathematics

Mathematics, 21.06.2019 12:30

As soon as look at the parallelogram abcd shown below: the table below shows the steps to prove that if the quadrilateral abcd is a parallelogram, then its opposite sides are congruent: which choice completes the missing information for reason 5 in the chart? (6 points) congruent parallelograms congruent triangles similar angles similar triangles

Answers: 1

Answer

Mathematics, 21.06.2019 17:00

If a baby uses 15 diapers in 2 days how many diapers will the baby use in a year

Answers: 2

Answer

Mathematics, 21.06.2019 19:00

Billy plotted −3 4 and −1 4 on a number line to determine that −3 4 is smaller than −1 4 .is he correct? explain why or why not

Answers: 3

Answer

Mathematics, 21.06.2019 22:30

There are 93 calories in a small candy bar how many calories are ther in a half dozen small candy bars?