Question

Given that we love to learn about science and medicine, we are going to collect the brains of 10 deceased zombies; you are given that this sample is simple and random. You are to test that the mean volume of these zombie brains is less than 1,000 cm3. Because this is important, you are to use ? = 0.01. Use this data: {660, 715, 721, 848, 912, 942, 998, 1002, 1155, 1197}. (Demonstrate all 5 hypothesis testing steps, and only use p-value and confidence intervals.)

Answer 1

Here we want to test"whether the mean volume of zombie brains is less than 1,000 cm3 or not"

So the null hypothesis and the alternative hypothesis are as follows:

Here sample size is less than 30 , also population standard deviation is not known, so we need to assume that the sample comes from the normal distribution and then we can use one sample t test.

The sample mean ( ) and the sample standard deviation( s ) by using excel are as

Formula of t test statistic is as

Degrees of freedom = n - 1 = 10 - 1 = 9

p-value = "=TDIST(1.474,9,1)" = 0.0873

Note that: here we use excel to find p-value, the command is "=TDIST( | t | , df, tails)

From the alternative hypothesis this is one tailed test

Decision rule:

1) If p-value < level of significance then we reject null hypothesis.

2) If p-value > level of significance then we fail to reject null hypothesis.

Here p-value = 0.0873 > 0.01 then we fail to reject the null hypothesis.

Conclusion: At 1% level of significance there is not sufficient evidence to say that the mean volume of zombie brains is less than 1,000 cm³