Answer to Question #175446 in Statistics and Probability for Denisse Bisuña

Question

1.Draw a normal curve showing the 99% confidence interval

2.Appliace manufacturers are required to post a sticker on their products regarding the electricity economy of each appliance for sale. Explain how this sticker indicates estimation in general.

3.Compare and contrast the z-distribution and the t-distribution.

4.Using t-table, give the confidence coefficients for each of the following:

a. n = 12 with 95% confidence

b. n = 15 with 95% confidence

c. n = 21 with 99% confidence

d. n = 23 with 95% confidence

e. n = 25 with 99% confidence

5.Assuming that the samples come from normal distributions, find the margin of error E given the following:

a. n = 10 and X = 28 with s = 4.0, 90% confidence

b. n = 16 and X = 50 with s = 4.2, 95% confidence

c. n = 20 and X = 68.2 with s = 2.5, 90% confidence

d. n = 23 and X = 80.6 with s = 3.2, 95% confidence

e. n = 25 and X = 92.8 with s = 2.6, 99% confidence

6.Using the information in number 3, find the interval estimates of the population mean.

a.

b.

c.

d.

e.

Answer 1

1.

2.

Dark green, it represents consumption of less than 25%.

With its intermediate green colour, it symbolizes consumption of less than 30%.

Its pale green colour represents consumption estimated as from 30% to 42%.

Yellow in colour, it offers average consumption between 42% and 55%.

Identified by the colour orange, it represents consumption of between 55% and 75%.

Bright orange in colour, it represents a consumption level of between 75% and 90%

Red in colour, it indicates that it has a consumption level of between 90% and 100%.

3.

The distribution curves are both​ mound-shaped and symmetric. ​ However, the​ t-test statistic curve is flatter than the​ z-statistic curve because the​ t-test is much more sensitive to the sample size. The standard normal or z-distribution assumes that you know the population standard deviation. The t-distribution is based on the sample standard deviation.

4.a) $t=1.78$

b) $t=1.75$

c) $t=2.52$

d) $t=1.71$

e) $t=2.49$

5.

$E=z_{\alpha}\frac{s}{\sqrt{n}}$

a.

$E=1.65\cdot\frac{4}{\sqrt{10}}=2.087$

b.

$E=1.96\cdot\frac{4.2}{\sqrt{16}}=2.058$

c.

$E=1.65\cdot\frac{2.5}{\sqrt{20}}=0.922$

d.

$E=1.96\cdot\frac{3.2}{\sqrt{23}}=1.308$

e.

$E=2.58\cdot\frac{2.6}{\sqrt{25}}=1.3416$

6.

$z_{\alpha/2}<\frac{X-\mu}{s/\sqrt{n}}<z_{1-\alpha/2}$

$(X-z_{\alpha/2}\cdot s/\sqrt{n})>\mu>(X-z_{1-\alpha/2}\cdot s/\sqrt{n})$

a.

$(28+2.575\cdot4/\sqrt{10})>\mu>(28-1.645\cdot4/\sqrt{10})$

$25.92<\mu<31.26$

b.

$(50-1.96\cdot4.2/\sqrt{16})<\mu<(50+1.96\cdot4.2/\sqrt{16})$

$47.94<\mu<52.06$

c.

$(68.2-1.645\cdot2.5/\sqrt{20})<\mu<(68.2+2.575\cdot2.5/\sqrt{20})$

$67.28<\mu<69.64$

d.

$(80.6-1.96\cdot3.2/\sqrt{23})<\mu<(80.6+1.96\cdot3.2/\sqrt{23})$

$79.29<\mu<81.91$

e.

$(92.8-2.575\cdot2.6/\sqrt{25})<\mu<(92.8+2.575\cdot2.6/\sqrt{25})$

$91.46<\mu<94.14$