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ElenaW [278]
3 years ago
12

A random sample of 20 students yielded a mean of ¯x = 72 and a variance of s2 = 16 for scores on a college placement test in mat

hematics. Assuming the scores to be normally distributed, construct a 98% confidence interval for σ2.
Mathematics
1 answer:
Helen [10]3 years ago
7 0

Answer:

The 98% confidence interval for the variance in the pounds of impurities would be 8.400 \leq \sigma^2 \leq 39.827.

Step-by-step explanation:

1) Data given and notation

s^2 =16 represent the sample variance

s=4 represent the sample standard deviation

\bar x represent the sample mean

n=20 the sample size

Confidence=98% or 0.98

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 mean or variance 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.

The Chi square distribution is the distribution of the sum of squared standard normal deviates .

2) Calculating the confidence interval

The confidence interval for the population variance is given by the following formula:

\frac{(n-1)s^2}{\chi^2_{\alpha/2}} \leq \sigma^2 \leq \frac{(n-1)s^2}{\chi^2_{1-\alpha/2}}

On this case the sample variance is given and for the sample deviation is just the square root of the sample variance.

The next step would be calculate the critical values. First we need to calculate the degrees of freedom given by:

df=n-1=20-1=19

Since the Confidence is 0.98 or 98%, the value of \alpha=0.02 and \alpha/2 =0.01, and we can use excel, a calculator or a table to find the critical values.  

The excel commands would be: "=CHISQ.INV(0.01,19)" "=CHISQ.INV(0.99,19)". so for this case the critical values are:

\chi^2_{\alpha/2}=36.191

\chi^2_{1- \alpha/2}=7.633

And replacing into the formula for the interval we got:

\frac{(19)(16)}{36.191} \leq \sigma^2 \leq \frac{(19)(16)}{7.633}

8.400 \leq \sigma^2 \leq 39.827

So the 98% confidence interval for the variance in the pounds of impurities would be 8.400 \leq \sigma^2 \leq 39.827.

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90/3=30

3 0
3 years ago
Help me on this I really need it
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Answer:


Step-by-step explanation:

Given that sale of grills increase 6% per year

CUrrent sale of grills this year = 3300

So in the first year sales would increase by 3300(6%)

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This will be again increasing by 6% in II year and so on.

Hence we have

every year 3300 increases by 6% compoundly

So

No of sales in t year

=3300(1+0.06)^t\\=3300(1.06^t)

In 6th year sale

s(6) =3300(1.06)^6\\=4681.11

7 0
3 years ago
A ball is thrown from an initial height of 2 feet with an initial upward velocity of 31 ft/s. The ball's height h (in feet) afte
Vlad1618 [11]

A quadratic equation is in the form of ax²+bx+c. The time at which the height of the ball is 16 feets is 0.717 seconds and 1.221 seconds.

<h3>What is a quadratic equation?</h3>

A quadratic equation is an equation whose leading coefficient is of second degree also the equation has only one unknown while it has 3 unknown numbers. It is written in the form of ax²+bx+c.

The complete question is:

A ball is thrown from an initial height of 2 feet with an initial upward velocity of 31 ft/s. The ball's height h (in feet) after 7 seconds is given by the following, h=2+31t-16t². Find all values of t for which the ball's height is  16 feet. Round your answer(s) to the nearest hundredth.

The time at which the height of the ball is 16 feet can be found by,

h = 2 + 31t - 16t²

16 = 2 + 31t - 16t²

16 - 2 - 31t + 16t² = 0

16t² - 31t + 14 = 0

t = \dfrac{-(-31)\pm \sqrt{(-31)^2-4(16)(14)}}{2(16)}\\\\

t = 0.717 , 1.221

Hence, the time at which the height of the ball is 16 feets is 0.717 seconds and 1.221 seconds.

Learn more about Quadratic Equations:

brainly.com/question/2263981

#SPJ1

4 0
2 years ago
Find the measure of angle A
Westkost [7]

Answer:

35 degrees

Step-by-step explanation:

Sum of angles inside a triangle is 180 degrees.

Right angle is 90 degrees.

180 = 90 + (x + 46) + (x + 66) = 2x + 202

x = -11

A = x + 46 = -11 + 46 = 35

6 0
3 years ago
Target is selling a particular toaster oven that costs $27 and is marked up 45% based on cost. Find the markup amount and the se
DENIUS [597]

Step-by-step explanation:

markup amount = 45% of $27

=> 45/100 * $27

=> $12.15

Now,

selling price = $27 + $12.15 => $39.15

6 0
2 years ago
Read 2 more answers
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