Question

In: Statistics and Probability

You are interested in the weight gain of the Auburn Freshman. You think that the average...

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):

20, 9, 16, 8, 10, 11, 20, 15, 9, 16, 10, 8, 6, 6, 10, 14, 14, 16, 14, 9

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:

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:

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¯= ________

(d) Evaluate the test statistic

T=x¯−μ0s/n‾√.

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? _________ (yes or no)

(h) Is the weight gain significantly different from 15 lbs? ________ (yes or no)

Solutions

Expert Solution

a) Null Hypothesis: The weight gain is equal to 15 pounds.

Alternative Hypothesis: The weight gain is not equal to 15 pounds.

b) From the sample data we get -

Sample mean = x bar = 12.05

c) Sample Standard deviation s = 4.2361

d) Test statistic = t = -3.114 (Rounded to 3 decimal places)

e) The test statistic is t-distributed with n - 1 = 20-1 = 19 degrees of freedom.

f) P value = 0.0057 (Rounded to 4 decimal places)

g) Here P value < hence we reject the null hypothesis.

YES

f) YES

Hope this will help you. Thank you :)

orchestra answered 2 years ago

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