A group of 300 housewives was interviewed to determine if there is a preference for one of two detergents. Detergent A was favor
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Answer:
If we compare the p value and a significance level assumed we see that
so we can conclude that we can reject the null hypothesis, and the true mean is significantly different from 100 at 5% of significance.
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 to be tested
We need to conduct a hypothesis in order to determine if the mean is different from 100, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
Compute the test statistic
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".
We can replace in formula (1) the info given like this:
Now we need to find the degrees of freedom for the t distirbution given by:
Conclusion
Since is a tao tailed test the p value would be:
If we compare the p value and a significance level assumed we see that
so we can conclude that we can reject the null hypothesis, and the true mean is significantly different from 100 at 5% of significance.