Mathematics, 22.04.2020 04:44 bjbass899

Scores on the SAT Mathematics test are believed to be normally distributed. The scores of a simple random sample of five students who recently took the exam are 570, 620, 710, 540 and 480. We want to find a 95% confidence interval of the population mean of SAT math scores. Calculate the point estimate.

Answers: 2

Show answers

Answers

Answer from: janelisse199820

The mean calculated for this case is $\bar X=584$

And the 95% confidence interval is given by:

$584-2.776\frac{86.776}{\sqrt{5}}=476.271$

$584+2.776\frac{86.776}{\sqrt{5}}=691.729$

So on this case the 95% confidence interval would be given by (476.271;691.729)

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size

Solution to the problem

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

In order to calculate the mean and the sample deviation we can use the following formulas:

$\bar X= \sum_{i=1}^n \frac{x_i}{n}$ (2)

$s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}}$ (3)

The mean calculated for this case is $\bar X=584$

The sample deviation calculated s=86.776

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

df=n-1=5-1=4

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a tabel to find the critical value. The excel command would be: "=-T.INV(0.025,4)".And we see that $t_{\alpha/2}=2.776$

Now we have everything in order to replace into formula (1):

$584-2.776\frac{86.776}{\sqrt{5}}=476.271$

$584+2.776\frac{86.776}{\sqrt{5}}=691.729$

So on this case the 95% confidence interval would be given by (476.271;691.729)

Answer from: Quest

one of each metals

step-by-step explanation:

Answer from: Quest

to determine the unit cost your would divide the total cost by the number sold.

7 bagels for $4.41 $4.41/7 = $.63 each at fresh side

5 bagels for $3.60 $3.60/5 = $.72 each at value mart

Another question on Mathematics

Mathematics, 21.06.2019 16:00

Drag the tiles to the correct boxes to complete the pairs. not all tiles will be used. the heights of the girls in an advanced swimming course are 55, 60, 59, 52, 65, 66, 62, and 65 inches. match the measures of this data with their values.

Answers: 1

Answer

Mathematics, 21.06.2019 19:30

When 142 is added to a number the result is 64 more times the number my options are 35 37 39 41

Answers: 1

Answer

Mathematics, 21.06.2019 22:40

The value of x in this system of equations is 1. 3x + y = 9 y = –4x + 10 substitute the value of y in the first equation: combine like terms: apply the subtraction property of equality: apply the division property of equality: 3x + (–4x + 10) = 9 –x + 10 = 9 –x = –1 x = 1 what is the value of y?

Answers: 1

Answer

Mathematics, 21.06.2019 23:00

Pls the last one and it has to be like number 6

Answers: 2

Answer

You know the right answer?

Scores on the SAT Mathematics test are believed to be normally distributed. The scores of a simple r...

Questions