If you flip a pair of coins 48 times, how many times are you most likely to get 2 heads.

Researchers are interested in the effect of a certain nutrient on the growth rate of plant seeding. Use a hydroponics grow proce

Rashid [163]

Answer:

The 95% confidence interval for the mean would be given by (56.604;68.596)

The 99% confidence interval for the mean would be given by (53.196;72.004)

Step-by-step explanation:

1) Previous concepts

When we compute a confidence interval for the mean, we are interested on the parameter population mean, and we use the info from the sample to estimate this parameter.

2) Basic operations

The sample mean can be calculated with the following formula

$\sum_{i=1}^n \frac{x_i}{n}$

Using excel we can use this function to calculate the mean:

=AVERAGE(54.2,59.8,61.8,63.3,65.1,71.4)

The value obtained is $\bar X=62.6$

In order to find the sample deviation we can use this formula

$s=\sqrt{\sum_{i=1}^n \frac{(x_i-\bar X)^2}{n-1}}$

And using excel we can use this function to calculate the sample standard deviation:

=STDEV.S(54.2,59.8,61.8,63.3,65.1,71.4)

The value obtained is $s=5.713$

The sample size for this case is n=6, n<30 so then is better use the t distribution to calculate the margin of error. First we need to calculate the degrees of freedom, on this case $df=n-1=6-1=5$

The formula for the confidence interval would be given by:

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

3) Part a

If we want a 95% or 0.95 of confidence, then the value for the signficance is $\alpha=1-0.95=0.05$ , and $\alpha/2=0.025$ , and $1-\frac{\alpha}{2}=0.975$ so we can find the critical t value with the following formula in excel:

=T.INV(0.975,5)

And we got $t_{\alpha/2}= 2.571$

And we can replace into equation (1) and we got:

$62.6 \pm 2.571\frac{5.713}{\sqrt{6}}$

And using excel with the following formulas we got:

=62.6-2.571*(5.713/SQRT(6)) = 56.604

=62.6+2.571*(5.713/SQRT(6)) = 68.596

So the 95% confidence interval for the mean would be given by (56.604;68.596)

4) Part b

If we want a 99% or 0.99 of confidence, then the value for the signficance is $\alpha=1-0.99=0.01$ , and $\alpha/2=0.005$ , and $1-\frac{\alpha}{2}=0.995$ so we can find the critical t value with the following formula in excel:

=T.INV(0.995,5)

And we got $t_{\alpha/2}= 4.032$

And we can replace into equation (1) and we got:

$62.6 \pm 4.032\frac{5.713}{\sqrt{6}}$

And using excel with the following formulas we got:

=62.6-4.032*(5.713/SQRT(6)) = 53.196

=62.6+4.032*(5.713/SQRT(6)) = 72.004

So the 99% confidence interval for the mean would be given by (53.196;72.004)

8 0

2 years ago

Find a value of x that is a solution to 5(x – 3) = x + 13. Describe how you found the solution.

Ann [662]

Answer:

x=7

because distributive property and addition and subtraction

7 0

2 years ago

Read 2 more answers

Can someone help me :> IF RIGHT...WILL GET DA CROWN UwU

Alex787 [66]

Answer:

$2\ \frac{1}{2}$ $or$ $2.5$

Step-by-step explanation:

$--------------------------------------------$

$1\ \frac{1}{4}+1\ \frac{1}{4}$ = $?$

$or$

$2\cdot1\ \frac{1}{4}$ = $?$

$--------------------------------------------$

$It$ $equals$ $2\ \frac{1}{2}$ $inches$

$--------------------------------------------$

<em>Hope this helps! <3</em>

$--------------------------------------------$

8 0

2 years ago

One number is 8 times another number. The numbers are both positive and have a difference of 70. Find the numbers. Which of the

worty [1.4K]

Let, the first (smaller) number = x
Larger number = 8x
Then, 8x - x = 70
7x = 70
x = 70/7
x = 10
& 8(10) = 80

In short, Your Numbers would be, 10 & 80

Hope this helps!

4 0

2 years ago

5. what is the theoretical probability that a coin toss results in one head and one tail showing?

Alenkasestr [34]

There are two sides (heads and tails). So one head would be 1/2, and one tail would also be 1/2.

4 0

2 years ago