Answer:
If we compare the p value and a significance level assumed for example we see that
so we can conclude that we FAIL to reject the null hypothesis, and the actual true mean for the scores is NOT significant less than 78.
Step-by-step explanation:
Data given and notation
represent the sample mean
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.
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 determine if the mean is less than 78, 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 P-value
First we need to find the degrees of freedom given by:
Since is a one-side left tailed test the p value would be:
Conclusion
If we compare the p value and a significance level assumed for example we see that
so we can conclude that we FAIL to reject the null hypothesis, and the actual true mean for the scores is NOT significant less than 78.
