Question

0.98 0.95 1.64- Normal Quantile Plot 0.9 1.28 - 0.8 0.67 - 0.7 0.6 0.5 04 0.3 -0.67 - 0.2 0.1 - 1.28 - 0.05 - 1.64 0.02 20 15 Count 10 5 0 2 4 00 10 0

Can this be considered a normal distribution, or does the data point between 0 and 2 affect it? I am trying to do a t test and the p-value is <0.0001, alpha=0.05, but I assume that I can't do a t-test on it because it is not normally distributed (symmetrical, unimodal, no outliers, mean in the middle). In short, can I do a t-test on this data?

Answer 1

From the histogram, the total frequencies or count is greater than 30. So the sampling distribution of the sample mean under the assumption of standard deviation is unknown follows t-distribution. So you can apply t-test.

For large n ( > 30) and population standard deviation is not given then we use t-distribution to test the hypothesis of population mean.