Question

Using the table for many repetitions of the experiment of tossing a coin 10 times, what is the mean number of heads in 50 repetitions of this experiment and 500 repetitions, and which of these sample means is closer to the population mean?


Number of Heads 0 1 2 3 4 5 6 7 8 9 10
In 50 Repetitions 0 0 1 5 9 16 10 6 2 1 0
In 200 Repetitions 0 2 8 22 38 55 41 24 9 1 0
In 500 Repetitions 2 5 24 57 111 111 110 56 21 3 0
In 1,000 Repetitions 1 8 43 117 207 248 203 121 45 6 1


x bar equals 4.8, 5.03; 50 repetitions are closer to the population mean
x bar equals 4.9, 4.99; 50 repetition

Answer 1

can you help!?!? @John_ES

Answer 2

I am reading and thinking about it ;)

Answer 3

please ill give you a medal!

Answer 4

im timed on the question but please can you try to help me @John_ES

Answer 5

Ok, it was easier than I was thinking at first.

Answer 6

oh okay

Answer 7

You should calculate the mean using the definition,
\[\overline{x}=\sum\frac{x_if_i}{N}\]For the first case, you have
\[\overline{x}=4.94\] And the second,
\[\overline{x}=5.2\] Then, you can choose your answer because the mean for the experiment is
\[\mu=np=10\cdot0.5=5\] So you must choose the x that is closer to this value.

Answer 8

is C the closest?

Answer 9

When I say the first case, I mean, the 50 repetitions. The second case is the 500 repetitions.

Answer 10

Yes, C is the closest.

Answer 11

Do you understand how I calculated the means?

Answer 12

no i dont sorry

Answer 13

this question is kinda the same equation right?

Answer 14

Using the table, I use the formula,
\[\overline{x}=\sum\frac{x_if_i}{N}\]
In the case of 50 repetitionis, N=50. x_i is the number of heads, and f_i is the number of times you obtain this heads. So for N=50, using the table you have,
\[\overline{x}=(2*1 + 3*5 + 4*9 + 5*16 + 6*10 + 7*6 + 8*2 + 9)/50=5.2\]And for N=500, you have,
\[\overline{x}=(2*0 + 1*5 + 2*24 + 3*57 + 4*111 + 5*111 + 6*110 + 7*56 + 8*21 +
9*3)/500=4.94\]

Answer 15

ohhhh yeah i get it now how you found the mean

Answer 16

Yes, is somewhat different. In the problem the formulas you should use are written.

Answer 17

yeah so how do i solve it then, idk what numbers to use

Answer 18

First, calculate SD, using the highest and lowest amounts. Tell me your result.

Answer 19

so $200-$140 right?

Answer 20

i mean $200 - $75

Answer 21

Yes, and then divide by 6, using the formula they provide.

Answer 22

125/6 = 20.8

Answer 23

Ok. Now apply the second formula using N=500, the number of students.

Answer 24

1.86

Answer 25

Perfect! you have your answer.

Answer 26

oh wow thank you and this last one im sorry

Answer 27

Tell me.

Answer 28

i really wanna understand this so i can do the rest on my own

Answer 29

so i added everything to the formula and got 0.017

Answer 30

\[2*\sqrt{.72(1-.72/2500}\]

Answer 31

Yes, that's perfect!

Answer 32

i did it right?!?!?

Answer 33

no way ! thank god

Answer 34

However, remember that in this case
p=0.28
1-p=0.72

Answer 35

In the formula that doesn't matter. But you should remember that the problem stays that the proportion of yes is "p", and the proportion of "no" is q=1-p.

Answer 36

ohhhh okay yeah i understand

Answer 37

thank you so much

Answer 38

you really did help

Answer 39

You're welcome.