Mathematics, 29.11.2019 05:31 zitterkoph

In a study of speed dating, male subjects were asked to rate the attractiveness of their female dates, and a sample of the results is listed below (1equalsnot attractive; 10equalsextremely attractive). construct a confidence interval using a 99% confidence level. what do the results tell about the mean attractiveness ratings of the population of all adult females? 6, 9, 3, 9, 6, 6, 7, 7, 8, 9, 3, 8

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Answer from: leannaadrian

The 99% confidence interval is be given by (4.872;8.628)

Step-by-step explanation:

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".

The dataset is:

6, 9, 3, 9, 6, 6, 7, 7, 8, 9, 3, 8

2) Compute the sample mean and sample standard deviation.

In order to calculate the mean and the sample deviation we need to have on mind the following formulas:

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

The value obtained is $\bar X=6.75$

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

The sample deviation obtained is s=2.094

3) Find the critical value t* Use the formula for a CI to find upper and lower endpoints

In order to find the critical value we need to take in count that our sample size n =12 <30 and on this case we don't know about the population standard deviation, so on this case we need to use the t distribution. Since our interval is at 99% of confidence, our significance level would be given by $\alpha=1-0.99=0.01$ and $\alpha/2 =0.005$ . The degrees of freedom are given by:

df=n-1=12-1=11

We can find the critical values in excel using the following formulas:

"=T.INV(0.005,11)" for $t_{\alpha/2}=-3.106$

"=T.INV(1-0.005,11)" for $t_{1-\alpha/2}=3.106$

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

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

The next step would be calculate the limits for the interval

Lower interval :

$\bar X - t_{\alpha/2}\frac{s}{\sqrt{n}}$

$6.75 - 3.106 \frac{2.094}{\sqrt{12}}=4.872$

Upper interval :

$6.75 + 3.106 \frac{2.094}{\sqrt{12}}=8.628$

So the 99% confidence interval would be given by (4.872;8.628)

99% of the time, when we calculate a confidence interval with a sample of n=12, the true mean of rate of attractiveness of their female dates will be between the 4.872 and 8.628.

Answer from: Quest

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step-by-step explanation:

Answer from: Quest

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