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Is the sample different than the population for Social Conformity of college students?

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A researcher knows that the population mean among college students taking the Social Conformity Test is a "neutral" 100. (scores higher than 100 are assumed to represent more conformity than average, and those lower than 100 indicate less conformity). A random sample of 30 students was selected, and the following values were recorded:

sample mean = 103
sample standard deviation= 10.83

Is this sample significantly different than the population?
State the null and alternative hypotheses.

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Solution Summary

With clear explanations and calculations, the problem is solved.

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Let mu be the population mean.

Null hypothesis H0: mu=100
Alternative hypothesis Ha: mu is NOT 100.

Use z-test, as the sample size ...

Solution provided by:
Changping Wang, MA
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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