California Is a Beautiful Place to Live, but It Is$\pm$

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The Answer is a. H_o: Sample mean = population mean
H_A: Sample mean does not equal population mean.
b. 100 - 1 = 99
c. NOTE: Because it is 2-tailed, you must have a plus-minus critical value. This means that if your calculated, or observed, t value is either greater than 2.000 or less than -2.000, your result will be statistically significant. Also note that I used 60 degrees of freedom in Appendix B rather than 120. Even though 99 is closer to 120 than it is to 60, go with the smaller number when you have a df between two numbers. If your results are significant at the smaller df, they will be significant at the larger df.
d. First I need to calculate a standard error of the mean:
s_x= 3/?100

\rightarrow

3/10

\rightarrow

.30

t₀ = (6 - 5)/.30

\rightarrow

1/.30

\rightarrow

3.33.
e. I am going to REJECT the null hypothesis because my observed t value exceeds my critical t value. IN other words, 3.33>2.000, so reject the null hypothesis
f. Yes.
g. The chances of obtaining my results by chance were less than 5% (p < alpha), therefore I decide my results are statistically significant.
h. CI₉₅ = 6

\rightarrow

(.30) (2.000)

\rightarrow

6

\rightarrow

.60

\rightarrow

5.40, 6.60. I am 95% confident that the average level of happiness in the population of Californians is between 5.40 and 6.60. Notice how this interval does not include the population mean of Americans, which was 5? We already knew this because our result was statistically significant, meaning that the sample mean was different from the population mean at the .05 level. Also notice that our population we are talking about in this confidence interval is the population of CALIFORNIANS. We are concluding that the population of Californians differs in happiness from the population of Americans. Notice how we used sample data to reach a conclusion about populations? That is the crux of inferential statistics.

California Is a Beautiful Place to Live, but It Is $\pm$

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California Is a Beautiful Place to Live, but It Is ±\pm±

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California Is a Beautiful Place to Live, but It Is $\pm$

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