When birth weights were recorded for a simple random sample of 14 male babies born to mothers in a region taking a special vitamin​ supplement, the sample had a mean of 3.658 kilograms and a standard deviation of 0.666 kilograms. Use a 0.05 significance level to test the claim that the mean birth weight for all male babies of mothers given vitamins is different from 3.39 ​kilograms, which is the mean for the population of all males in this particular region. Based on these​ results, does the vitamin supplement appear to have an effect on birth​ weight?

t=

​(Round to three decimal places as​ needed.)

Find the​ P-value.

​P-value=

Expert