Question

You are interested in the weight gain of the Auburn Freshman. You think that the average weight gain of the Auburn Freshman student is not 15 pounds. You collect a random sample of measurements. The weight gains are (a negative value indicates a weight loss):

9, 19, 10, 18, 14, 11

You may assume for the following questions that the distribution of weight gain is normal.

(a) State the appropriate hypothesis test. (This was done before collecting the data)

Null Hypothesis (answer options): The weight gain is less than 15 pounds/The weight gain is at most 15 pounds/The weight gain is equal to 15 pounds/The weight gain is not equal to 15 pounds/The weight gain is at least 15 pounds/The weight gain is greater than 15 pounds.

Alternative Hypothesis(answer options) : The weight gain is less than 15 pounds/The weight gain is at most 15 pounds/The weight gain is equal to 15 pounds/The weight gain is not equal to 15 pounds/The weight gain is at least 15 pounds/The weight gain is greater than 15 pounds.

(b) Calculate the sample mean x¯.x¯=

(c) Calculate the sample standard deviation s.s=

(d) Evaluate the test statistic

T=

(e) The test statistic is t-distributed with_______ degrees of freedom.

(f) The p-value for the test is _______.

(g) Should you reject the null hypothesis in favor of the alternative at significance level α=0.01?

(h) Is the weight gain significantly different from 15 lbs?

Answer 1

a. Here claim is that the average weight gain of the Auburn Freshman student is not 15 pounds.

So hypothesis is The weight gain is equal to 15 pounds/The weight gain is not equal to 15 pounds

b. Sample mean is

c. For standard deviation

Create the following table.

data	data-mean	(data - mean)2
9	-4.5	20.25
19	5.5	30.25
10	-3.5	12.25
18	4.5	20.25
14	0.5	0.25
11	-2.5	6.25

Find the sum of numbers in the last column to get.

So

d. Test statistics is

e. Here t distribution is having 5 df

f. P value is TDIST(0.87,5,2)=0.4241

g. As P value is greater than α=0.01, we fail to reject the null hypothesis.