diff --git a/exercises/_19-sa-inference-one-mean.qmd b/exercises/_19-sa-inference-one-mean.qmd index a6fd6f67..e26348c6 100644 --- a/exercises/_19-sa-inference-one-mean.qmd +++ b/exercises/_19-sa-inference-one-mean.qmd @@ -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.