Discussion:
Q: At Western University the historical mean of scholarship examination scores for freshman applications is 900. A historical population standard deviation σ = 180 is assumed known. Each year, the assistant dean uses a sample of applications to determine whether the mean examination score for the new freshman applications has changed.
a. State the hypotheses.
b. Using the scores for a sample of applicants below, compute a 95% confidence interval estimate of the population mean examination score for the new freshman class.
c. Use the confidence interval to conduct a hypothesis test. Use a = .05. What is your conclusion?
d. What is the p-value?
| Score |
| 719 |
| 1314 |
| 634 |
| 882 |
| 953 |
| 723 |
| 923 |
| 856 |
| 575 |
| 1093 |
| 1051 |
| 888 |
| 1130 |
| 626 |
| 923 |
| 662 |
| 756 |
| 826 |
| 854 |
| 1085 |
| 918 |
| 1091 |
| 941 |
| 990 |
| 958 |
| 670 |
| 863 |
| 1253 |
| 1269 |
| 1147 |
| 746 |
| 808 |
| 933 |
| 838 |
| 978 |
| 849 |
| 1154 |
| 807 |
| 1158 |
| 1169 |
| 1147 |
| 765 |
| 837 |
| 882 |
| 987 |
| 1014 |
| 856 |
| 854 |
| 1015 |
| 856 |
| 672 |
| 972 |
| 974 |
| 1185 |
| 989 |
| 988 |
| 1000 |
| 750 |
| 1048 |
| 1314 |
| 815 |
| 1073 |
| 809 |
| 781 |
| 953 |
| 966 |
| 913 |
| 964 |
| 859 |
| 756 |
| 902 |
| 785 |
| 974 |
| 1302 |
| 1136 |
| 996 |
| 933 |
| 898 |
| 776 |
| 1263 |
| 906 |
| 1103 |
| 982 |
| 794 |
| 942 |
| 1235 |
| 1096 |
| 674 |
| 1125 |
| 913 |
| 743 |
| 1117 |
| 861 |
| 820 |
| 1094 |
| 698 |
| 794 |
| 914 |
| 905 |
| 1022 |
| 478 |
| 884 |
| 1178 |
| 828 |
| 657 |
| 921 |
| 1006 |
| 1267 |
| 713 |
| 951 |
| 1082 |
| 968 |
| 1024 |
| 839 |
| 889 |
| 1028 |
| 1020 |
| 803 |
| 929 |
| 905 |
| 1112 |
| 750 |
| 817 |
| 905 |
| 1025 |
| 624 |
| 926 |
| 1352 |
| 1316 |
| 805 |
| 750 |
| 835 |
| 575 |
| 934 |
| 773 |
| 530 |
| 1041 |
| 901 |
| 801 |
| 1015 |
| 851 |
| 884 |
| 1046 |
| 877 |
| 1006 |
| 1432 |
| 1176 |
| 795 |
| 951 |
| 930 |
| 959 |
| 708 |
| 660 |
| 676 |
| 949 |
| 1016 |
| 798 |
| 924 |
| 750 |
| 979 |
| 908 |
| 554 |
| 1190 |
| 1038 |
| 899 |
| 738 |
| 1027 |
| 1043 |
| 956 |
| 796 |
| 989 |
| 873 |
| 935 |
| 1098 |
| 1067 |
| 803 |
| 773 |
| 1229 |
| 1365 |
| 813 |
| 887 |
| 958 |
| 1116 |
| 1090 |
| 694 |
| 1151 |
| 1153 |
| 1254 |
| 1161 |
| 1088 |
| 796 |
| 1076 |
| 756 |
| 933 |
| 959 |
| 1033 |
| 815 |
| 909 |
| 1094 |
| 749 |