Question 1/10

How much money do winners go home with from the television quiz show Jeopardy? To determine an answer, a random sample of winner

Liula [17]

Answer:

The 95% confidence interval would be given by (14444.04;33657.30)

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".

Data: $26,650 $6,060 $52,820 $8,490 $13,660$25,840 $49,840 $23,790 $51,480 $18,960$990 $11,450 $41,810 $21,060 $7,860

We can calculate the mean and the deviation from these data with the following formulas:

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

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

$\bar X=24050.67$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s=17386.13 represent the sample standard deviation

n=15 represent the sample size

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

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

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

$df=n-1=15-1=14$

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 tabel to find the critical value. The excel command would be: "=-T.INV(0.025,14)".And we see that $t_{\alpha/2}=2.14$

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

$24050.67-2.14\frac{17386.13}{\sqrt{15}}=14444.04$

$24050.67+2.14\frac{17386.13}{\sqrt{15}}=33657.30$

So on this case the 95% confidence interval would be given by (14444.04;33657.30)

6 0

2 years ago

Gael and Torin don't want to take the garbage out, but their mom said one of them had to. Gael suggests they flip 2 coins to det

Alexandra [31]

Possible outcomes :

Heads Heads

Heads Tails

Tails Tails

Tails Heads

Probability of matching : 2/4 = 0.5

Torin should agree since the proposal is fair

3 0

2 years ago

In this activity, you'll calculate a probability and use it to predict the result of repeating a simple chance-based trial many

kompoz [17]

1) The outcomes for rolling two dice, the sample space, is as follows:
(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6)
(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)
(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6)
(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)
(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6)
(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)
There are 36 outcomes in the sample space.
2) The ways to roll an odd sum when rolling two dice are:
(1, 2), (1, 4), (1, 6), (2, 1), (2, 3), (2, 5), (3, 2), (3, 4), (3, 6), (4, 1), (4, 3), (4, 5), (5, 2), (5, 4), (5, 6), (6, 1), (6, 3), (6, 5). There are 18 outcomes in this event.
3) The probability of rolling an odd sum is 18/36 = 1/2 = 0.5

3 0

2 years ago

Read 2 more answers

The given family of functions is the general solution of the differential equation on the indicated interval. find a member of t

Ilia_Sergeevich [38]

Try this option (see the attachment), if it is possible check result in other sources.

3 0

2 years ago

Read 2 more answers

A square rug covers 79 square feet of floor. What is the approximate length of one side of the rug? (Approximate to the nearest

Mice21 [21]

A = a^2.....where " a " is the length of one side
A = 79

79 = a^2...take sqrt of both sides, eliminating the ^2
sqrt 79 = a
8.89 = a

so the length of one side is approximately 8.89 ft <==

8 0

2 years ago