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Answer:
Since the calculated value is lower than the critical value we have enough evidence to FAIL to reject the null hypothesis
So then we can conclude that the population mean is not significantly higher than 100
Step-by-step explanation:
Data given and notation
represent the mean score for the sample
represent the 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 determine if the mean is higher than 100, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
We don't know the population deviation, so for this case 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:
Calculate the critical value
We need to find the degrees of freedom first, given by:
Since we are conducting a right tailed test we need to find a critical value on the t distribution with 24 degrees of freedom that accumulates 0.01 of the area on the right and we got:
Since the calculated value is lower than the critical value w have enough evidence to FAIL to reject the null hypothesis
So then we can conclude that the population mean is not significantly higher than 100