Calcium is essential to tree growth. In 1990, the concentration of calcium in precipitation in Chautauqua, New York, was 0.11 milligram per liter \( \left(\frac{\mathrm{mg}}{\mathrm{L}}\right) \). A random sample of 8 precipitation dates in 2018 results in the following data: \[ \begin{array}{lllll}0.234 & 0.313 & 0.108 & 0.065 & 0.087 \\ \text { A normal probability plot suggests the data could come from a population that is normally distributed. A boxplot does not show any } \\ \text { outliers. Does the sample evidence suggest that calcium concentrations have changed since 1990? Use the a }=0.01 \text { level of } \\ \text { significance. }\end{array} \] \( \mathrm{t}_{0}=1.41 \) (Round to two decimal placestas needed.) Find the P-value. P-value \( =\square \) (Round to three decimal places as needed.)

SAT scores are normally distributed with a mean of 1,500 and a standard deviation of 300 . An administrator at a college is interested in estimating the average SAT score of first-year students. If the administrator would like to limit the margin of error of the \( 96 \% \) confidence interval to 25 points, how many students should the administrator sample? Make sure to give a whole number answer.

pose that grade point averages of undergraduate students at one university have a bell-shaped distribution with a mean of 2.6 and a standard deviation of 0.42 cribe where approximately \( 95 \% \) of grade point averages lie. swer \[ \text { below } 1.76 \text { and above } 3.44 \] between 1.76 and 3.18 and above 3.02

Find the range of the following data set. Assume the data set is a sample.

You wish to test the following claim \( \left(H_{a}\right) \) at a significance level of \( \alpha=0.05 \) \[ \begin{array}{l}H_{o}: \mu=72.3 \\ H_{a}: \mu \neq 72.3\end{array} \] You believe the population is normally distributed, but you do not know the standard deviation. You obta a sample of size \( n=5 \) with mean \( M=78.2 \) and a standard deviation of \( S D=18.8 \). What is the p-value for this sample? (Report answer accurate to four decimal places.) -value \( =\square \)

5 The mean age for first 13 voters at Zwide Voting Station, is 40 and the standard deviation is 5. Comment by refering to the standard deviations on how the ages at Zwide Station compare to those at Dingiswayo Station.