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# Hypothesis Testing

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An astronomer is testing the claim that the mean brightness of a certain star is now more than 30 units. She is able to get 6 readings on the star during her experiment as shown in the table. Using &#945; = 0.01, does this indicate a new mean brightness of more than 30?

DATA

1 29
2 29
3 29
4 31
5 32
6 34

Assume that such readings are normally distributed.

PS: PLEASE SHOW ALL WORK AND EXPLAIN IN BASIC, BASIC TERMS. ALSO, I REQUEST FOR THE SAME TA (CHANGPING WANG, MA)

Sorry I 'M NOT SURE IF THIS IS A TWO-SAMPLE t TEST!

##### Solution Summary

The expert uses hypothesis testing to examine the mean brightness of a certain star. A normally distributed sample is provided.

##### Solution Preview

An astronomer is testing the claim that the mean brightness of a certain star is now more than 30 units. She is able to get 6 readings on the star during her experiment as shown in the table. Using α = 0.01, does this indicate a new mean brightness of more than 30?

DATA

1 29
2 29
3 29
4 31
5 32
6 34

Assume that such readings are normally distributed.

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###### 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!"
• "Thank you"
• "Thank you very much for your valuable time and assistance!"

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