Mathematics, 07.04.2020 23:01 wizewolf

The data below represent a random sample of 9 scores on a statistics quiz. (The maximum possible score on the quiz is 10.) Assume that the scores are normally distributed with a standard deviation of 2.3. Estimate the population mean with 95% confidence. 8,10,8,4,5,7,3,10,8 Note: For each confidence interval, enter your answer in the form (LCL, UCL). You must include the parentheses and the comma between the confidence limits. Confidence Interval

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Answer from: zackinator9226

$7-1.96\frac{2.3}{\sqrt{9}}=5.497$

$7+1.96\frac{2.3}{\sqrt{9}}=8.503$

So on this case the 95% confidence interval would be given by (5.497;8.503)

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)

$\sigma=2.3$ represent the population standard deviation

n represent the sample size

Solution to the problem

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

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (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 $\bar X=7$

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: "=-NORM.INV(0.025,0,1)".And we see that $z_{\alpha/2}=1.96$

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

$7-1.96\frac{2.3}{\sqrt{9}}=5.497$

$7+1.96\frac{2.3}{\sqrt{9}}=8.503$

So on this case the 95% confidence interval would be given by (5.497;8.503)

Answer from: Quest

step-by-step explanation:

Answer from: Quest

we have the parent function given by,

1. the function is translated 5 units to the left.

so, we get, becomes

2. the function is translated 5 units to the right.

so, we get, becomes

3. the function is translated 5 units upwards.

so, we get, becomes

4. the function is translated 5 units downwards.

so, we get, becomes

5. the function is reflected across x-axis.

so, we get, becomes

6. the function is reflected across y-axis.

so, we get, becomes .

step-by-step explanation:

mark brainliest.

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The data below represent a random sample of 9 scores on a statistics quiz. (The maximum possible sco...

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