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A sociologist was investigating the ages of grandparents of high school students. From a random sample of 10 high school student

umka2103 [35]

Answer:

$(69.8-71.6) -2.101 \sqrt{\frac{8.38^2}{10} +\frac{6.65^2}{10}}= -8.908$

$(69.8-71.6) +2.101 \sqrt{\frac{8.38^2}{10} +\frac{6.65^2}{10}}= 5.308$

So then the confidence interval for the difference of means is given by:

$-8.908 \leq \mu_M -\mu_F \leq 5.308$

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".

$\bar X_{M}= 69.8$ represent the mean for the age of grandmother

$\bar X_{F}= 71.6$ represent the mean for the age of grandfather

$s_{M}= 8.38$ represent the sample deviation for the age of grandmother

$s_{F}= 6.65$ represent the sample deviation for the age of grandfather

$n_M = n_F= 10$

Solution to the problem

For this case the confidence interval is given by:

$(\bar X_{M} -\bar X_F) \pm t_{\alpha/2} \sqrt{\frac{s^2_M}{n_M} +\frac{s^2_F}{n_F}}$

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

$df=n_M +n_F-2=10+10-2=18$

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,18)".And we see that $t_{\alpha/2}=2.101$

And replacing we got:

$(69.8-71.6) -2.101 \sqrt{\frac{8.38^2}{10} +\frac{6.65^2}{10}}= -8.908$

$(69.8-71.6) +2.101 \sqrt{\frac{8.38^2}{10} +\frac{6.65^2}{10}}= 5.308$

So then the confidence interval for the difference of means is given by:

$-8.908 \leq \mu_M -\mu_F \leq 5.308$

5 0

4 years ago

Select the statements that are true for the graph of y=(x+2)^2+4

likoan [24]

Alrigty

in form
$y=a(x-h)^2+k$
the vertex is (h,k)
the constant, a, deterimines the size and direction
if a>0, then the parabola opens up and the vertex is the minimum
if a<0 then the parabola opens down and the vertex is the maximum

so we are given
$y=1(x-(-2))^2+4$
1>0 so it opens up
vertex is (-2,4)
the vertex is a minimum

the vertex is (-2,4) and the graph has a minimum

3 0

3 years ago

Read 2 more answers

Completely Factor the expression -18 P - 9

jekas [21]

can i have brainliest pls tyyy :)))

Answer:

-9(2p+1)

Step-by-step explanation:

-18p - 9

find the GCF (greatest common factor) for the expression.

-9

then, divide each term by the GCF

-18p / -9 -9 / -9

= 2p = 1

next, put the two terms you get when dividing into the final form of the answer:

GCF on the outside and quotients on the inside

-9(2p+1)

hope this helped! ;)

5 0

4 years ago

Consider the division expression 7 ½ ÷ 2. Select all multiplication equations that correspond to this division expression.

Firlakuza [10]

Answer:

i dunno

Step-by-step explanation:

but i need the points to ask questions

4 0

3 years ago

Read 2 more answers

What value of “n” makes the equation true?

Doss [256]

Answer:

12 OR 1/12 (Check how you write your equations! Just look below for the one that it actually is lol)

Step-by-step explanation:

6 = (1/2)n

6/(1/2) = n

12 = n

OR

6 = 1/(2n)

6(2n) = 1

12n = 1

n = 1/12

6 0

3 years ago