What is the regular area of a trapezoid?
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Answer:
The probability that exactly 27 of 104 eligible voters voted is 0.057 = 5.7%.
Step-by-step explanation:
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
The standard deviation of the binomial distribution is:
Normal probability distribution
Problems of normally distributed distributions can be solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that ,
.
In this case, assume that 104 eligible voters aged 18-24 are randomly selected.
This means that .
Suppose a previous study showed that among eligible voters aged 18-24, 22% of them voted.
This means that
Mean and standard deviation:
Probability that exactly 27 voted
By continuity continuity, 27 consists of values between 26.5 and 27.5, which means that this probability is the p-value of Z when X = 27.5 subtracted by the p-value of Z when X = 26.5.
X = 27.5
has a p-value of 0.8621
X = 26.5
has a p-value of 0.8051
0.8621 - 0.8051 = 0.057
The probability that exactly 27 of 104 eligible voters voted is 0.057 = 5.7%.
Your answer is correct... , so
Then distributing to both terms on the right gives
Answer:
Now we can find the degrees of freedom:
Now we can calculate the p value with the alternative hypothesis using the following probability:
Using a significance level of 0.01 or 1% we have enough evidence to FAIL to reject the null hypothesis and we can conclude that shoppers participating in the loyalty program NOT spent more on average than typical shopper at this significance level assumed
Step-by-step explanation:
Information given
represent the sample mean
represent the sample standard deviation
sample size
represent the value to verify
t would represent the statistic
represent the p value
System of hypothesis
We want to verify if shoppers participating in the loyalty program spent more on average than typical shoppers (120) , the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
The statistic for this case is given by:
(1)
Replacing the info given we got:
Now we can find the degrees of freedom:
Now we can calculate the p value with the alternative hypothesis using the following probability:
Using a significance level of 0.01 or 1% we have enough evidence to FAIL to reject the null hypothesis and we can conclude that shoppers participating in the loyalty program NOT spent more on average than typical shopper at this significance level assumed