# Null & Alternative Hypotheses : T-Tests

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Ten people agree to take part in an experiment designed to determine whether a persons weight differs between morning & evening. Each person is weighed last thing at night & first thing in the morning, wearing the same clothes.

The results, giving weights in kilogrammes are below.

weight 1 2 3 4 5 6 7 8 9 10

night 70.5 61.0 27.5 55.0 65.0 64.0 50.0 31.0 45.5 41.0

morn 70.0 60.5 27.0 55.0 65.0 62.5 49.0 30.0 44.5 40.5

Is there any evidence of a difference in a persons weight between night & morning? State clearly the null & alternative hypotheses you are testing & any assumptions you have to make. Use a 1% level of significance.

Use minitab to do a 2-sample t-test & a paired t-test at the 1% level of significance to test the hypothesis that a persons weight in the morning is less than their weight at night. (Interpret the output)

Discuss the difference between the two tests.

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##### Solution Summary

Hypotheses based on given data are tested using t-tests. A Word file and an Excel file are included with this comprehensive solution.

###### Education

- BSc , Wuhan Univ. China
- MA, Shandong Univ.

###### Recent Feedback

- "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
- "excellent work"
- "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
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