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Sergio039 [100]
3 years ago
6

A sample with mean of 85 and SD of 12 is transformed into z-scores. After the transformation, what are the values for the mean a

nd standard deviation for the sample of z-scores
Mathematics
1 answer:
MrRa [10]3 years ago
5 0

Answer:

The value remain unchanged.

Step-by-step explanation:

By Z score, we mean:

Z = \frac{x-\mu}{\sigma}, if we substitute the given values of mean and standard deviation, we obtain the z score value. That is,

Z =  \frac{85 - 0}{12} = 85/12 = 7.083333.

NB: We assume that mean and standard deviation are in the same units.

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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.

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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.

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Hopes this helps:

Answer:

12 1/3
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