Question

\begin{tabular} Sheet \\ \hline \hline 285 \\ \hline 2.73 \\ \hline 2.43 \\ \hline 3.01 \\ \hline 2.4 \\ \hline 3.13 \\ \hline 2.81 \\ \hline 3.02 \\ \hline 3.10 \\ \hline 2.98 \\ \hline 294 \\ \hline 2.70 \\ \hline 2.41 \\ \hline 2.41 \\ \hline 3.05 \\ \hline 2.91 \\ \hline 2.70 \\ \hline 2.78 \\ \hline 3.11 \\ \hline 2.58 \\ \hline 3.18 \\ \hline 2.85 \\ \hline 3.01 \\ \hline 2.87 \\ \hline 2.92 \\ \hline 2.42 \\ \hline 2.68 \\ \hline 2.96 \\ \hline 2.33 \\ \hline 2.70 \\ \hline 2.65 \\ \hline 2.68 \\ \hline 2.93 \\ \hline 2.77 \\ \hline 2.71 \\ \hline 2.66 \\ \hline 2.78 \\ \hline 2.97 \\ \hline 2.83 \\ \hline 2.77 \\ \hline 3.16 \\ \hline 297 \\ \hline 2.66 \\ \hline 2.73 \\ \hline 294 \\ \hline 2.65 \\ \hline 2.94 \\ \hline 271 \\ \hline 285 \\ \hline 3.02 \\ \hline \end{tabular} \begin{tabular}{l} Sheet1 \\ \hline \end{tabular} \begin{tabular} \hline Sheet' \\ \hline \hline 11018.043 \\ \hline 10121.562 \\ \hline 10658.526 \\ \hline 11688.589 \\ \hline 11465.908 \\ \hline 10325.318 \\ \hline 11729.782 \\ \hline 11868.255 \\ \hline 12027.264 \\ \hline 10699.265 \\ \hline 10388.493 \\ \hline 11101.462 \\ \hline 10981.056 \\ \hline 11750.638 \\ \hline 10759.097 \\ \hline 11828.089 \\ \hline 10099.31 \\ \hline 13082.946 \\ \hline 11626.651 \\ \hline 10093.529 \\ \hline 10528.954 \\ \hline 11204.073 \\ \hline 11076.81 \\ \hline 12658.598 \\ \hline 10367.675 \\ \hline 12242.367 \\ \hline 10717.983 \\ \hline 10810.795 \\ \hline 10219.219 \\ \hline 9851.2983 \\ \hline 11716.237 \\ \hline 8186.5991 \\ \hline 9825.3434 \\ \hline 9663.8268 \\ \hline 8247.0955 \\ \hline 9146.5127 \\ \hline 10425.086 \\ \hline 9614.7231 \\ \hline 10673.586 \\ \hline 11619.608 \\ \hline 12171.412 \\ \hline 10863.203 \\ \hline 13967.702 \\ \hline 1118381.46 \\ \hline \end{tabular} \begin{tabular} \hline Sheet \\ \hline \hline 11402.976 \\ \hline 10990.749 \\ \hline 10332.816 \\ \hline 10586.459 \\ \hline 10624.189 \\ \hline 9559.7354 \\ \hline 10547.956 \\ \hline 10414.314 \\ \hline 12684.34 \\ \hline 9959.7841 \\ \hline 11496.497 \\ \hline 11268.453 \\ \hline 9278.4807 \\ \hline 10332.704 \\ \hline 10320.407 \\ \hline 9417.5568 \\ \hline 875.539 \\ \hline 9810.6465 \\ \hline 10248.654 \\ \hline 9487.0612 \\ \hline 10003.249 \\ \hline 9871.3038 \\ \hline 10807.868 \\ \hline 11549.007 \\ \hline 11487.163 \\ \hline 10839.902 \\ \hline 8610.6797 \\ \hline 10605.639 \\ \hline 10663.101 \\ \hline 11246.064 \\ \hline 11022.084 \\ \hline 10563.196 \\ \hline 11414.425 \\ \hline 12059.915 \\ \hline 10718.295 \\ \hline 9736.8194 \\ \hline 10395.281 \\ \hline 11462.003 \\ \hline 10384.621 \\ \hline 9687.0393 \\ \hline 10981.918 \\ \hline 11444.622 \\ \hline 11136.931 \\ \hline 9312.1452 \\ \hline 9915.5242 \\ \hline \end{tabular} \begin{tabular}c \hline Sheet' \\ \hline \hline 9587.105 \\ \hline 11156.533 \\ \hline 11383.368 \\ \hline 11634.747 \\ \hline 10835.286 \\ \hline 10807.727 \\ \hline 10650.633 \\ \hline 10563.099 \\ \hline 9868.9011 \\ \hline 10364.994 \\ \hline 11738.958 \\ \hline 9759.8076 \\ \hline 10529.298 \\ \hline 10848.86 \\ \hline 9005.4669 \\ \hline 12563.389 \\ \hline 10280.419 \\ \hline 10122.162 \\ \hline 11323.471 \\ \hline 10773.406 \\ \hline 10130.811 \\ \hline 10015.651 \\ \hline 10041.792 \\ \hline 11323.558 \\ \hline 10509.957 \\ \hline 10683.407 \\ \hline 9564.8698 \\ \hline 10335.604 \\ \hline 11163.975 \\ \hline 9766.9825 \\ \hline 11481.74 \\ \hline 10116.362 \\ \hline 12612.554 \\ \hline 10705.476 \\ \hline 10565.737 \\ \hline 11751.112 \\ \hline 11770.298 \\ \hline 11943.248 \\ \hline 10581.382 \\ \hline 10549.854 \\ \hline 12241.021 \\ \hline 10807.635 \\ \hline 10648.559 \\ \hline 10298.044 \\ \hline 11245.027 \\ \hline \end{tabular} Use Sheet 1 of the Excel file to answer the following questions, A school administrator believes that the mean class GPAs for a given course are higher than the prefen mean of 2.75 at a significance level of 0.05, and checks a randomly chosen sample of 50 classes. Cre histogram, and calculate x ˉ , the t-statistic, and the p-value. From the histogram, can normality be assumed? x ˉ = t= p= Since the p-value is han the significance level 0.05, the null hypothesis From the histogram, can normality be assumed? x ˉ = t= p= Since the p-value is han the significance level 0.05, the null hypothesis vidence exists that the mean GPA is greater than 2.75.

Answer 1

The administrator, based on a significance level of 0.05 and a sample of 50 classes, rejects the null hypothesis, providing evidence that the mean class GPAs are greater than 2.75.

Step-by-step explanation:

In analyzing the data, the administrator conducted a hypothesis test with a significance level of 0.05 on a random sample of 50 classes. The calculated p-value, representing the probability of obtaining results as extreme as the ones observed if the null hypothesis were true, was found to be less than 0.05.

Since the p-value is below the chosen significance level, the null hypothesis is rejected. This implies that there is statistical evidence to support the administrator's belief that the mean class GPAs for the given course are higher than the preferred mean of 2.75.

Understanding hypothesis testing involves comparing the p-value to the significance level, where a lower p-value indicates stronger evidence against the null hypothesis. In this case, the administrator's decision to reject the null hypothesis aligns with the conventional significance level of 0.05.