Discuss the below:
IQ scores for boys and girls (These data were collected by a researcher at Purdue University. Treat these data as simple random samples from all seventh-grade students in the district)
Q: Here are IQ test scores of 31 seventh-grade girls in a Midwest school district.
114 100 104 89 102 91 114 114 103 105
108 130 120 132 111 128 118 119 86 72
111 103 74 112 107 103 98 96 112 112
93
The IQ test scores of the 47 seventh-grade boys in the same district are:
111 107 100 107 115 111 97 112 104 106 113
109 113 128 128 118 113 124 127 136 106 123
124 126 116 127 119 97 102 110 120 103 115
93 123 79 119 110 110 107 105 105 110 77
90 114 106
a). Find the mean IQ scores for girls and for boys. It is common for boys to have somewhat higher scores on standardized tests. It that true?
b). Compute 95% T intervals of the Girls' IQ's and the Boys' IQ's and explain what these intervals mean.
c). Make a histogram for each set of data to determine whether each distribution is reasonably symmetric with no outliers. If this is so, we can use t- procedures-do your histograms indicate that we can use t-procedures?
d). Give a 90% 2-Sample T interval confidence for the mean difference between the mean IQ scores for all boys and girls in the district. Then explain what this interval means.