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Nadusha1986 [10]
3 years ago
7

Assume that both populations are normally distributed. ​a) Test whether mu 1 not equals mu 2 at the alpha equals 0.05 level of s

ignificance for the given sample data. ​b) Construct a 95​% confidence interval about mu 1 minus mu 2. Sample 1 Sample 2 n 19 19 x overbar 16.2 14.1 s 4.5 3.1
Mathematics
1 answer:
Radda [10]3 years ago
5 0

Answer:

(16.2-14.1) -2.03 \sqrt{\frac{4.5^2}{19} +\frac{3.1^2}{19}} = -0.445

(16.2-14.1) +2.03 \sqrt{\frac{4.5^2}{19} +\frac{3.1^2}{19}} = 4.645

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".

n_1 = 19 sample size 1

n_2 = 19 sample size 2

\\bar X_1 = 16.2 sample mean for group 1

\\bar X_2 = 14.2 sample mean for group 2

s_1 = 4.5 sample deviation for group 1

s_2 = 3.1 sample deviation for group 2

Solution to the problem

For this case the confidence interval is given by:

(\bar X_1 -\bar X_2) \pm t_{\alpha/2} \sqrt{\frac{s^2_1}{n_1} +\frac{s^2_2}{n_2}}

And the degrees of freedom are given by:

df = n_1 +n_2 -2 = 19+19 -2= 36

We want a 95% of confidence o then the significance level is 1-0.95 =0.05 and \alpha/2 = 0.025 if we find a critical value in the t distribution with 36 degrees of freedom we got:

t_{cric} =2.03

And replacing we got:

(16.2-14.1) -2.03 \sqrt{\frac{4.5^2}{19} +\frac{3.1^2}{19}} = -0.445

(16.2-14.1) +2.03 \sqrt{\frac{4.5^2}{19} +\frac{3.1^2}{19}} = 4.645

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13.41 x (5.4 divided by 9)
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The value of the expression will be 8.166.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The mathematical expression is,

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