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Fix formatting and clarify statistical analysis details #549

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Fix formatting and clarify statistical analysis details #549

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2 changes: 1 addition & 1 deletion exercises/_19-sa-inference-one-mean.qmd
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Expand Up @@ -23,7 +23,7 @@
\addtocounter{enumi}{1}

1. \(a\) $H_0$: $\mu = 8$ (New Yorkers sleep 8 hrs per night on average.)
$H_A$: $\mu \neq 8$ (New Yorkers sleep less or more than 8 hrs per night on average.) (b) Independence: The sample is random. The min/max suggest there are no concerning outliers. $T = -1.75$. $df=25-1=24$. (c) p-value $= 0.093$. If in fact the true population mean of the amount New Yorkers sleep per night was 8 hours, the probability of getting a random sample of 25 New Yorkers where the average amount of sleep is 7.73 hours per night or less (or 8.27 hours or more) is 0.093. (d) Since p-value $>$ 0.05, do not reject $H_0$. The data do not provide strong evidence that New Yorkers sleep more or less than 8 hours per night on average. (e) Yes, since we did not rejected $H_0$.
$H_A$: $\mu \neq 8$ (New Yorkers sleep less or more than 8 hrs per night on average.) (b) Independence: The sample is random. The min/max suggest there are no concerning outliers. $T = -1.75$. $df=25-1=24$. (c) p-value $= 0.093$. If in fact the true population mean of the amount New Yorkers sleep per night was 8 hours, the probability of getting a random sample of 25 New Yorkers where the average amount of sleep is 7.73 hours per night or less (or 8.27 hours or more) is 0.093. (d) Since p-value $>$ 0.05, do not reject $H_0$. The data do not provide strong evidence that New Yorkers sleep more or less than 8 hours per night on average. (e) Yes, since we did not reject $H_0$.
\addtocounter{enumi}{1}

1. With a larger critical value, the confidence interval ends up being wider. This makes intuitive sense as when we have a small sample size and the population standard deviation is unknown, we should have a wider interval than if we knew the population standard deviation, or if we had a large enough sample size.
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