A neuroimaging researcher has the hypothesis that individuals who eat Captain Cr

Question

A neuroimaging researcher has the hypothesis that individuals who eat Captain Crunch cereal have smaller brain volumes than the populations. To test this, he has calculated brain volumes for a sample of Captain Crunch eaters. Here are the data (measured in cubic centimeters (cc)):

1030           1221
1120           1140
1002           992
1199           1098
999           1011
1321           959
1200           1450
1070           1188

In the population, the mean brain volume is 1250 cc with a standard deviation of 300 cc. Assume that alpha = 0.01 and use hypothesis testing to examine the researcher’s hypothesis.

Explanation / Answer

Here, H0 : mu > = 1250

Ha : mu <1250

Calculate x bar by taking the average sample of data

X bar = 1132.375

test satistic;

t = (x bar - mu ) / (SD/ sqrt(n))

= (1132.375 - 1250) / ( 300 / sqrt(16))

= -1.56

Now, we need to find p value by using degree of freedom= n -1 = 16 -1 = 15 and t statistic value = -1.56

here, p value = 0.069 , So, Pvalue > alpha value

We failed to reject the null hypothesis.

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