If anyone is fluent in statistics, help a brother out. I know how to do this pro

Question

If anyone is fluent in statistics, help a brother out. I know how to do this problem, except I'm confused about finding the degrees of freedom.The question is:

"The Bureau of Labor Statistics (BLS) reported from a random sample that the mean amount spent by [group] in 2001 on [product] was $177. How large a sample size would have been required if BLS had wanted to estimate the population mean amount spent by [group] within a Margin of Error of $50 with 95% confidence. The sample standard deviation is $150."

I know that ybar = 177, E=50, ta/2 = 0.025 (before df and t-chart applied), and s=150. When I'm looking at the answer document, it shows that ta/2 after df according to the t-chart is 2.00, which can correlate directly to df=60 (2.000) or be (in my opinion, wrongly) simplified from df=50 (2.009). Still, any insight on finding degrees of freedom (df) directly from this word problem and not by using the formula?

The answer is n=36.

Explanation / Answer

if the observations are more than 30 means the table value of t at 0.025 with >30 d.f. is almost 1.96 .

1.96 means you can take approxmately 2

there fore you can choose d.f. arbitrarly more than >=30(30,50,...)

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