Question

Run a one sample t-test for HGHTI_P to test if the CHIS sample is significantly different from 68(the average height in the U.S.).

What can you conclude based on the results of your test (Hint: what does the p-value tell you?)? Do you reject the null hypothesis, or fail to reject the null hypothesis? Does the CHIS sample population have a statistically significant different average height than 68 inches tall?

Answer 1

Of course, this is a case of 1-sample t-test because you are given a sample of CHIS. You have to compare this sample mean to the average height in the U.S. Another thing is you are not given with variance of the population so you will have to estimate the sample variance from the given sample. Therefore, in this particular situation t-test is suitable test to apply.

First and foremost step is to define your hypothesis.

Ho(null hypothesis): mean=64 inches

Now, to know what is 1-sample t-test and how to apply the same?

The t test tells you how significant the differences between the sample mean and population mean are in the case of unknown variance,that is , it lets you know if those differences (measured in means/averages) could have happened by chance.

The test statistic is given by-

   

where xbar= sample mean (calculate from the given sample)

mu= population mean(hypothesis mean)

s= sample standard deviation(While calculating the sample variance, you would divide it by (n-1) instead of n)

n= sample size

The larger the t-statisitc, the more difference there is between. The smaller the t-statistic, the more similarity there is between.

P-value:The p-value is the level of significance within a statistical hypothesis test representing the probability of the occurrence of a given event(difference between means). The p-value is used to find a rejection points to provide the smallest level of significance at which the null hypothesis would be rejected. P-value tells that how likely is the difference observed in your sample data if the null hypothesis is true?

P-value= Probability(>t-value)

Lower the p-value: higher the difference observed

Higher the p-value: lesser the difference observed

Decision: Let the given level of significance is 5%. then

If p-value <0.05 then reject null hypothesis that is,  the CHIS sample have a statistically significant different average height than 68 inches tall.

and if p-value >0.05 then you would fail to reject null hypothesis.

Thanks