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3 years ago

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A simple random sample of 20 third-grade children from a certain school district is selected, and each is given a test to measur

e his/her reading ability. You are interested in calculating a 95% confidence interval for the population mean score. In the sample, the mean score is 64 points, and the standard deviation is 12 points.
What is the margin of error associated with the confidence interval?

A. 2.68 points

B. 4.64 points

C. 5.62 points

D. 6.84 point

1 answer:

ICE Princess25 [194]3 years ago

4 0

Answer:

Option C) 5.62 points

Step-by-step explanation:

We are given the following in the question:

Sample size, n = 20

Sample mean score = 64

Sample standard deviation, s = 12

Degree of freedom =

$=n-1\\=20-1\\=19$

We have to calculate margin of error for a 95% confidence interval.

Formula for margin of error:

$t_{critical}\times \displaystyle\frac{s}{\sqrt{n}}$

Putting the values, we get,

$t_{critical}\text{ at degree of freedom 19 and}~\alpha_{0.05} = \pm 2.093$

$2.093\times (\displaystyle\frac{12}{\sqrt{20}} )\\\\ =5.6161\approx 5.62$

Thus, the correct answer is

Option C) 5.62 points

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Answer:

We conclude that there is no difference in potential mean sales per market in Region 1 and 2.

Step-by-step explanation:

We are given that a random sample of 12 supermarkets from Region 1 had mean sales of 84 with a standard deviation of 6.6.

A random sample of 17 supermarkets from Region 2 had a mean sales of 78.3 with a standard deviation of 8.5.

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$\mu_2$ = mean sales per market in Region 2.

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Alternate Hypothesis, $H_A$ : > $\mu_1-\mu_2\neq$ 0 {means that there is a difference in potential mean sales per market in Region 1 and 2}

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T.S. = $\frac{(\bar X_1 -\bar X_2)-(\mu_1-\mu_2)}{s_p \times \sqrt{\frac{1}{n_1}+ {\frac{1}{n_2}}} }$ ~ $t__n_1_+_n_2_-_2$

where, $\bar X_1$ = sample mean sales in Region 1 = 84

$\bar X_2$ = sample mean sales in Region 2 = 78.3

$s_1$ = sample standard deviation of sales in Region 1 = 6.6

$s_2$ = sample standard deviation of sales in Region 2 = 8.5

$n_1$ = sample of supermarkets from Region 1 = 12

$n_2$ = sample of supermarkets from Region 2 = 17

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