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Complete Question
A recent CBS News survey reported that 64% of adults felt the U.S. Treasury should continue making pennies. Suppose we select a sample of 18 adults.
a-1. How many of the 18 would we expect to indicate that the Treasury should continue making pennies
a-2) What is the standard deviation?
a-3) What is the likelihood that exactly 3 adults would indicate the Treasury should continue making pennies?
Answer:
a-1
a-2
a-3
Step-by-step explanation:
From the question we are told that
The sample size is
The proportion of adult that felt the U.S. Treasury should continue making pennies is p = 0.64
The proportion of adult that feel otherwise is
The mean is mathematically evaluated as
substituting values
The standard deviation is mathematically represented as
substituting values
The likelihood that 3 adult would indicate the Treasury should continue making pennies is mathematically evaluated as
Now
substituting values
So
Answer:
If we compare the p value and the significance level given we see that
so we can conclude that we have enough evidence to fail reject the null hypothesis, so we can't reject the claim that the true mean is at least 24 mpg (null hypothesis) at 1% of signficance.
Step-by-step explanation:
Data given and notation
represent the sample mean
represent the sample standard deviation for the sample
sample size
represent the value that we want to test
represent the significance level for the hypothesis test.
t would represent the statistic (variable of interest)
represent the p value for the test (variable of interest)
State the null and alternative hypotheses.
We need to conduct a hypothesis in order to check if the mean is lower than 24 (rejecting the claim proposed), 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
The first step is calculate the degrees of freedom, on this case:
Since is a one sided test the p value would be:
Conclusion
If we compare the p value and the significance level given we see that
so we can conclude that we have enough evidence to fail reject the null hypothesis, so we can't reject the claim that the true mean is at least 24 mpg at 1% of signficance.