Aliyah wants to evenly separate her super bouncy balls among 8 of her

A 95% confidence interval for a population mean is computed from a sample of size 400. Another 95% confidence interval will be c

Anna [14]

Answer:

The interval from the sample of size 400 will be approximately <u>One -half as wide</u> as the interval from the sample of size 100

Step-by-step explanation:

From the question we are told the confidence level is 95% , hence the level of significance is

$\alpha = (100 - 95 ) \%$

=> $\alpha = 0.05$

Generally from the normal distribution table the critical value of $\frac{\alpha }{2}$ is

$Z_{\frac{\alpha }{2} } = 1.96$

Generally the 95% confidence interval is dependent on the value of the margin of error at a constant sample mean or sample proportion

Generally the margin of error is mathematically represented as

$E = Z_{\frac{\alpha }{2} } * \frac{\sigma}{\sqrt{n} }$

Here assume that $Z_{\frac{\alpha }{2} } \ and \ \sigma \$ is constant so

$E = \frac{k}{\sqrt{n} }$

=> $E \sqrt{n} = K$

=> $E_1 \sqrt{n}_1 = E_2 \sqrt{n}_2$

So let $n_1 = 400$ and $n_2 = 100$

=> $E_1 \sqrt{400} = E_2 \sqrt{100}$

=> $E_1 = \frac{\sqrt{100} }{\sqrt{400} } E_2$

=> $E_1 = \frac{1}{2 } E_2$

So From this we see that the confidence interval for a sample size of 400 will be half that with a sample size of 100

7 0

2 years ago

This k12 question i need help

Yuri [45]

Answer: It's 72.

Step-by-step explanation: They deleted my answer <:(

4 0

2 years ago

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The ratio of girls to boys in the junior high band is 5 to 7. At the beginning of year, there were 72 students in the band. By t

rusak2 [61]

Ratio is 5girls:7boys with total 72 students
5+7= 12
72➗12= 6
6(5:7)= 30 girls : 42 boys

New ratio is 3:4 with 48 boys

48➗4= 12

So for girls 3x12= 36

So started with 30 girls ended with 36 girls... 6 girls joined band during the school year.

7 0

3 years ago

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from a group of 10 men and 8 women, 5 people are to be selected for a committee so that at least 4 men are on the committee. how

yaroslaw [1]

Only 1 way and that is to have 4 men and 1 woman

4 0

3 years ago

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Henri had a plum tree. The first week it was 15 feet. 2 weeks after that is was 22 feet and 2 more weeks later is was 36 feet. w

Alex

Answer:

The equation of tree's growth is given as : C(n) = 15 + 7 n ,

n = pair of weeks, n = 2, 4, 6 , 8 , ....

Step-by-step explanation:

Here, the initial height of the plum tree = 15 ft

⇒h (0) = 15 ft

Now, after two weeks the tree is 22 ft

⇒h (2) = 22 ft

Now,the growth of tree in 2 weeks

= Height after 2 weeks - Initial height of tree

= 22 ft - 15 ft = 7 ft

So, the plum tree grows 7 ft in 2 weeks

⇒ The plum tree grown (7/2) ft in 1 week.

Also, the growth of tree in next 2 weeks = 36 ft

So, the growth of tree in next 2 weeks

= Height after 4 weeks - Height after 2 weeks

= 36 ft - 22 ft = 14 ft

So, the tree grows 14 ft in next two weeks.

⇒ The tree grows 7 ft in next 2 weeks.

hence, the complete growth of each week is given as:

15 ft , 18.5 ft , 22 ft , 29 ft , 36 ft

So, the equation of tree' growth is given as : C(n) = 15 + 7 n

Here, n = Pair of weeks, n = 2, 4, 6 , 8 , ....

8 0

3 years ago