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____ [38]
1 year ago
11

Or dylan, an nfl running back, rushed for an average of 88 yards per game this season, which is 20% lower than his average was l

ast season. what was his average then?
Mathematics
1 answer:
faltersainse [42]1 year ago
3 0
His previous average was 96 yards per game
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A study was conducted to measure the effectiveness of hypnotism in reducing pain. The measurements are centimeters on a pain sca
saul85 [17]

Answer:

The 95% confidence interval for the difference would be given by (-1.776;0.376)

We are 95% confidence that the true mean difference is between -1.776 \leq \mu_d \leq 0.376. Since the confidence interval contains the value 0, we don't have enough evidence to conclude that hypnotism appear to be effective in reducing pain.

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".

Let put some notation  

x=test value before , y = test value after

x: 6.4 2.6 7.7 10.5 11.7 5.8 4.3 2.8

y: 6.7 2.4 7.4 8.1 8.6 6.4 3.9 2.7

The differences defined as d_i = y_i -x_i and we got:

d: 0.3, -0.2, -0.3, -2.4, -3.1, 0.6, -0.4, -0.1

We can calculate the mean and the deviation for the sample with the following formulas:

\bar d=\frac{\sum_{i=1}^n d_i}{n}

s_d =\frac{\sum_{i=1}^n (d_i -\bar d)^2}{n-1}

\bar d=-0.7 represent the sample mean for the difference

\mu_d population mean (variable of interest)

s_d=1.32 represent the sample standard deviation

n=8 represent the sample size  

Confidence interval

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

\bar d \pm t_{\alpha/2} *\frac{s_d}{\sqrt{n}}  (1)

In order to calculate the critical value t we need to find first the degrees of freedom, given by:

df=n-1=8-1=7

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 table to find the critical value. The excel command would be: "=-T.INV(0.025,8)".And we see that t_(\alpha/2)=2.306

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

-0.7-2.306\frac{1.32}{\sqrt{8}}=-1.776    

-0.7+2.306\frac{1.32}{\sqrt{8}}=0.376    

So on this case the 95% confidence interval for the difference would be given by (-1.776;0.376)

We are 95% confidence that the true mean difference is between -1.776 \leq \mu_d \leq 0.376. Since the confidence interval contains the value 0, we don't have enough evidence to conclude that hypnotism appear to be effective in reducing pain.

6 0
3 years ago
The manager of a coffee shop has one type of coffee that sells for $7 per pound and another type that sells for $11 per pound. T
kirza4 [7]
More of the $7 coffee would be used<span />
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3 years ago
Y=4x-2 y= 3x+1? What’s the (x,y)?
erik [133]
Idk this cause my teacher. Any teach
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3 years ago
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F(x) = x + 7<br> and<br> g(x) = x2<br> What is g( f(-9))
Tanya [424]

Answer:

4

Step-by-step explanation:

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2 years ago
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Five more than a twice a number is less than 20. If the number is a whole number, what could the number be?
SOVA2 [1]

Answer:

C

Step-by-step explanation:

5 more than twice a number

(A number)=variable=x

2x+5<20

Subtract 5 from both sides

2x<15

Divide by 2

x<7.5

Any number below 7.5 (can't be 7.5 though)

5 0
3 years ago
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