Esther wants to have $150,000 in 10 years. She plans to invest $18,000 to start and make yearly payments of $2,500 to the accoun
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Answer:
Null hypothesis:
Alternative hypothesis:
Two tailed test
So we reject the null hypothesis is or if
Our calculated value is not on the rejection zone so then we don't have enough evidence to reject the null hypothesis at 0.01 of significance for this case.
Step-by-step explanation:
Data given and notation
represent the sample mean
represent the population standard deviation
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 equal to 54 or no, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
If we analyze the size for the sample is > 30 but and we know the population deviation so is better apply a 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:
Decision rule
Since we are conducting a bilateral test we need to find a value on the normal standarrd distribution that accumulates 0.005 of the area on each tail. And we can use the following excel code: "=NORM.INV(0.005;0;1)"
So we reject the null hypothesis is or if
Our calculated value is not on the rejection zone so then we don't have enough evidence to reject the null hypothesis at 0.01 of significance for this case.