The difference of twice a number and three is
1 answer:
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Answer:
C. H 0:μ=5.00km H1:μ≠5.00km
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 to reject the null hypothesis, so we can conclude that the true mean is nto significantly different from 5.00.
Step-by-step explanation:
Some previous concepts
The p-value is the probability of obtaining the observed results of a test, assuming that the null hypothesis is correct.
A z-test for one mean "is a hypothesis test that attempts to make a claim about the population mean(μ)".
The null hypothesis attempts "to show that no variation exists between variables or that a single variable is no different than its mean"
The alternative hypothesis "is the hypothesis used in hypothesis testing that is contrary to the null hypothesis"
Data given and notation
represent the average for the sample
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.
z 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 population mean is equal to 5.00, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
Since the sample size >30 and large, the estimator for the population deviation would be s, and we can use the z test to compare the actual mean to the reference value, and the statistic is given by:
(1)
z-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
Since is a two tailed test the p value would be:
In Excel we can us ethe following formula to find the p value "=2*(1-NORM.DIST(1.978;0;1;TRUE))"
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 to reject the null hypothesis, so we can conclude that the true mean is nto significantly different from 5.00.