Use the diagram of circle C to answer the question.

From the data given, we estimate the population mean and population standard deviation. Then, we use this estimate to find a 95% confidence interval for the population variance and the population standard deviation.

Sample:

Salaries in millions of dollars: 2.2, 1.5, 0.5, 1.3, 2.4, 1.5, 2.7, 0.3, 2.0, 0.3

Question a:

The mean is the sum of all values divided by the number of values. So

$\overline{x} = \frac{2.2 + 1.5 + 0.5 + 1.3 + 2.4 + 1.5 + 2.7 + 0.3 + 2.0 + 0.3}{10} = 1.42$

The sample mean salary is of 1.42 million.

Question b:

The standard deviation is the square root of the difference squared between each value and the mean, divided by one less than the number of values.

So

$s = \sqrt{\frac{(2.2-1.42)^2 + (1.5-1.42)^2 + (0.5-1.42)^2 + (1.3-1.42)^2 + (2.4-1.42)^2 + (1.5-1.42)^2 + (2.7-1.42)^2 + ...}{9}} = 0.8772$

Thus, the estimate for the population standard deviation is of 0.8772 million.

Question c:

The sample size is $n = 10$

The significance level is $\alpha = 1 - 0.05 = 0.95$

The estimate, which is the sample standard deviation, is of $s = 0.8772$ .

Now, we have to find the critical values for the Pearson distribution. They are:

$\chi^2_{\frac{\alpha}{2},n-1} = \chi^2_{0.025,9} = 19.0228$

$\chi^2_{1-\frac{\alpha}{2},n-1} = \chi^2_{0.975,9} = 2.7004$

The confidence interval for the population variance is:

$\frac{(n-1)s^2}{\chi^2_{\frac{\alpha}{2},n-1}} < \sigma^2 < \frac{(n-1)s^2}{\chi^2_{1-\frac{\alpha}{2},n-1}}$

$\frac{9*0.8772^2}{19.0228} < \sigma^2 < \frac{9*0.8772^2}{2.7004}$

$0.3641 < \sigma^2 < 2.5646$

Thus, the 95% confidence interval for the population variance is (0.3641, 2.5646)

Question d:

Standard deviation is the square root of variance, so:

$\sqrt{0.3641} = 0.6034$

$\sqrt{2.5646} = 1.6014$

The 95% confidence interval for the population standard deviation is (0.6034, 1.6014).

For more on confidence intervals for population mean/standard deviation, you can check brainly.com/question/13807706

4 0

3 years ago

A recent drug survey showed an increase in use of drugs and alcohol among local high school students as compared to the national

prisoha [69]

Answer:

The answer is "0.586"

Step-by-step explanation:

Please find the solution to the given question:

$z= \frac{0.65-0.61}{\sqrt{\frac{0.65 \times 0.35}{100}+\frac{0.61 \times 0.39}{100}}}$

$= \frac{0.04}{\sqrt{\frac{0.2275}{100}+\frac{0.2379}{100}}}\\\\= \frac{0.04}{\sqrt{0.002275+0.002379}}\\\\= \frac{0.04}{\sqrt{0.004654}}\\\\= \frac{0.04}{0.0682202316}\\\\=0.586336327\\\\$

8 0

3 years ago

The designers of drink cartons must consider the length of the straw required so that it will reach the bottom

daser333 [38]

Answer:

The length of the straw is 13.53 cm

Step-by-step explanation:

Rectangular Prism

A rectangular prism or cuboid is a box-shaped object. It has six flat faces and all angles are right angles. And all of its faces are rectangles.

If the straw must reach into the diagonally opposite corners of the base of the carton, then its minimum length is calculated by:

$d^2= a^2+b^2+c^2$

Where a,b, and c are the dimensions of the cuboid. The image shows the dimensions of the drink carton: a=6 cm, b=10 cm, c=4 cm (order is not important), thus:

$d^2= 6^2+10^2+4^2=36+100+16=152$

$d=\sqrt{152}$

d= 12.33 cm

The straw must stick out of the carton by an additional 1.5 cm, thus the total length of the straw is: 12.33 + 1.5 = 13.53 cm

4 0

3 years ago

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