1:40 A.M to 3:01 A.M

The mean weight of 10 randomly selected newborn babies at a local hospital is 7.14 lbs and the standard deviation is 0.87 lbs. A

sergejj [24]

Answer:

a) $ME= 1.83 \frac{0.87}{\sqrt{10}}=0.5035$

b) 90% of all samples of size 10 have sample means within 0.5035 of the population mean.

c) The 90% confidence interval would be given by (6.636;7.643)

d) Yes, since the lower limit for the 90% confidence interval is higher than the value of 6.5 we can conclude that the true mean is significantly higher than 6.5 at 10% of significance. (6.636>6.5)

e) If we increase the confidence level that implies increase the margin of error. Since with more confidence level the value for the critical value $t_{\alpha/2}$ increase. So then the new interval would be wider than the original.

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".

$\bar X=7.14$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s=0.87 represent the sample standard deviation

n=10 represent the sample size

Part a

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

And the margin of error is given by:

$ME= t_{\alpha/2}\frac{s}{\sqrt{n}}$

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=10-1=9$

Since the Confidence is 0.90 or 90%, the value of $\alpha=0.1$ and $\alpha/2 =0.05$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.05,9)".And we see that $t_{\alpha/2}=1.83$

$ME= 1.83 \frac{0.87}{\sqrt{10}}=0.5035$

Part b

90% of all samples of size 10 have sample means within 0.5035 of the population mean.

Part c

Now we have everything in order to replace into formula (1):

$7.14-1.83\frac{0.87}{\sqrt{10}}=6.637$

$7.14+1.83\frac{0.87}{\sqrt{10}}=7.643$

So on this case the 90% confidence interval would be given by (6.636;7.643)

Part d

Yes, since the lower limit for the 90% confidence interval is higher than the value of 6.5 we can conclude that the true mean is significantly higher than 6.5 at 10% of significance. (6.636>6.5)

Part e

If we increase the confidence level that implies increase the margin of error. Since with more confidence level the value for the critical value $t_{\alpha/2}$ increase. So then the new interval would be wider than the original.

7 0

4 years ago

(5 points) An urn contains two blue balls denoted by B1 and B2, and three white balls denoted by W1, W2 and W3. One ball is draw

never [62]

Answer:

The probability of the event that first ball that is drawn is blue is $\frac 25$ .

Step-by-step explanation:

Probability:

If S is is an sample space in which all outcomes are equally likely and E is an event in S, then the probability of E,denoted P(E) is

$P(E)=\frac{\textrm{The number of outcomes E}}{\textrm{The total number outcomes of S}}$

Given that,

An urn contains two balls B₁ and B₂ which are blue in color and W₁,W₂ and W₃ which are white in color.

Total number of ball =(2+3) =5

The number ways of selection 2 ball out of 5 ball is

=5²

=25

Total outcomes = 25

List of all outcomes in the event that the first ball that is drawn is blue are

B₁B₁ , B₁B₂ , B₁W₁ , B₁W₂ , B₁W₃ , B₂B₁ , B₂B₂ , B₂W₁ , B₂W₂ , B₂W₃

The number of event that the first ball that is drawn is blue is

=10.

The probability of the event that first ball that is drawn is blue is

$=\frac{10}{25}$

$=\frac25$

3 0

4 years ago

Line r and m are parallel. Find the value of x.

vladimir2022 [97]

Answer:

Answer:

10x-3=7x+45 corresponding angle

10x-7x=45+3

3x=48

x=48/3=16

value of x is 16.

8 0

3 years ago

Is it ever too late to save for retirement?

Mekhanik [1.2K]

It can be too late to save for retirement. You want to begin saving at least 45 years before you plan to retire.

<h3>When to start savings for retirement?</h3>

Retirement is when labour stops working at a regular job. When a person retires, they would have a reduced source of income. This is why it is important to save for retirement. The earlier one starts to save for retirement, the more money the person would have when they retire.

To learn more about retirement, please check: brainly.com/question/20751552

#SPJ1

7 0

3 years ago

A herd of zebra currently has 45 members. Based on the available resources, biologists estimate that the size of the herd will i

Masja [62]

In this case, the zebra growth will increase 7% every year which means the growth will increase every year since its count from total population. When there is increased in growth, that will make the graph not linear.
With x-axis represent year and y-axis represent number of zebras, the graph will quadratic graph ( U-shape)

7 0

3 years ago