The table below shows head length and breadth of siblings. The four variables are X₁= head length of first son, X₂ = head breadth of first son, X3 = head length of second son, and X₁ = head breadth of second son obtained from 25 families. Do first and second sons differ in their average head dimensions? State appropriate null hypothesis for this and test at a = 0.05 and interpret results. You may use softwares for computations but make sure to give (X₁-X3 and state Ho in terms of Y. all necessary details. Hint: Define Y (X₂-X₁) Table 1: Head dimension data from Frets (1921), measured on siblings in 25 families X₁ X3 191 179 195 201 185 188 171 192 190 189 197 187 179 181 183 176 208 189 197 188 192 186 179 195 202 194 163 195 186 181 175 192 174 176 197 190 X₂ 155 149 148 153 144 157 150 159 152 150 161 147 153 160 154 137 155 153 145 140 154 143 139 167 153 183 174 190 188 161 183 173 182 165 185 178 176 200 187 145 152 149 149 142 152 149 152 159 151 158 147 150 159 151 130 158 148 146 137 152 147 143 158 150

A least squares line for a sample with 11 observations has an SSE = 192; calculate and s. Please show your work So i can understand how you arrived at the answer

Hello, When I sum up the variance, I'm getting 2.75. And not 1.65.  Also, how did you get the xi-mean in each column?  Thanks

The mean height of a certain kind of plant is 170 centimeters. Suppose we want to carry out a hypothesis test to see if the mean height when these plants are treated with a certain chemical differs from 170. State the null hypothesis H0 and the alternative hypothesis H1 that we would use for this test.

Before every​ flight, the pilot must verify that the total weight of the load is less than the maximum allowable load for the aircraft. The aircraft can carry 43 ​passengers, and a flight has fuel and baggage that allows for a total passenger load of 7,009 lb.  The pilot sees that the plane is full and all passengers are men. The aircraft will be overloaded if the mean weight of the passengers is greater than 7,009 lb / 43 =163 lb.  What is the probability that the aircraft is​ overloaded? Should the pilot take any action to correct for an overloaded​ aircraft? Assume that weights of men are normally distributed with a mean of 182.4 lb and a standard deviation of 38.4.

Before every​ flight, the pilot must verify that the total weight of the load is less than the maximum allowable load for the aircraft. The aircraft can carry 37 ​passengers, and a flight has fuel and baggage that allows for a total passenger load of 5,994lb. The pilot sees that the plane is full and all passengers are men. The aircraft will be overloaded if the mean weight of the passengers is greater than 5,994/37lb=162lb. What is the probability that the aircraft is​ overloaded? Should the pilot take any action to correct for an overloaded​ aircraft? Assume that weights of men are normally distributed with a mean of 181.6lb and a standard deviation of 36.2. The probability is approximately?

Before every flight, the pilot must verify that the total weight of the load is less than the maximum allowable load for the aircraft.  The aircraft can carry 42 passengers,  and a flight has fuel and baggage that allows for the total passenger load of 6,972lb. The pilot sees that the plane is full and all the passengers are men. The aircraft will be overloaded if the mean weight of the passengers is greater than 6,972lb/42=166lb. What is the probability that the aircraft is overloaded? Should the pilot take any action to correct for an overloaded aircraft? Assume that the weights of men are normally distributed with a mean of 176.9lb and a standard deviation of 37.7. THE probability is approximately.               ? Round to four decimal places.