Which is the best estimate of the sum of 56.78+5.06
1 answer:
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Answer:
The probability distribution is shown below.
Step-by-step explanation:
The urn consists of 8 white (<em>W</em>), 4 black (<em>B</em>) and 2 orange (<em>O</em>) balls.
The winning and losing criteria are:
- Win $2 for each black ball selected.
- Lose $1 for each white ball selected.
There are 8 + 4 + 2 = 14 balls in the urn.
The number of ways to select two balls is, ways.
The distribution of amount won or lost is as follows:
Outcomes: WW WO WB BB BO OO
X: -2 -1 1 4 2 0
Compute the probability of selecting 2 white balls as follows:
The number of ways to select 2 white balls is, ways.
The probability of WW is,
Compute the probability of selecting 1 white ball and 1 orange ball as follows:
The number of ways to select 1 white ball and 1 orange ball is, ways.
The probability of WO is,
Compute the probability of selecting 1 white ball and 1 black ball as follows:
The number of ways to select 1 white ball and 1 black ball is, ways.
The probability of WB is,
Compute the probability of selecting 2 black balls as follows:
The number of ways to select 2 black balls is, ways.
The probability of BB is,
Compute the probability of selecting 1 black ball and 1 orange ball as follows:
The number of ways to select 1 black ball and 1 orange ball is, ways.
The probability of BO is,
Compute the probability of selecting 2 orange balls as follows:
The number of ways to select 2 orange balls is, ways.
The probability of OO is,
The probability distribution of <em>X</em> is:
Outcomes: WW WO WB BB BO OO
X: -2 -1 1 4 2 0
P (X): 0.3077 0.1758 0.3516 0.0659 0.0879 0.0110
Answer:
We need to conduct a hypothesis in order to check if the high school students are representative of the overall population (or if the true mean is 1020 or not), the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
Step-by-step explanation:
Previous concepts and data given
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".
represent the sample mean
represent the sample standard deviation
n=144 represent the sample selected
significance level
State the null and alternative hypotheses.
We need to conduct a hypothesis in order to check if the high school students are representative of the overall population (or if the true mean is 1020 or not), the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
If we analyze the size for the sample is > 30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:
(1)
t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".
Calculate the statistic
We can replace in formula (1) the info given like this:
P-value
First we need to calculate the degrees of freedom given by:
Then since is a two sided test the p value would be:
Conclusion
If we compare the p value and a significance level for example we see that
so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the population mean is significant different from 1020 at 5% of significance.