Please solve with all information text required 1 BMW wishes to ascertain the mean repair costs for its cars in head on collisions at 25 mph In crash tests, only small samples are feasible so BMW decides to crash only five of its cars under the stated conditions The repair costs (in dollars) are 797 571 904 1147 418 Find the average cost of the five crashes Find the standard deviation of the cost for the five crashes Using the above data, BMW wishes to obtain a range of values that will encompass the true mean repair cost Since they wish to use this for advertising purposes, they need to be nearly certain, in particular , 95 certain, the range of value will encompass the true mean repair cost Consequently, they need to construct a 95 confidence interval for the true mean repair cost Towards, this end, carry out the construction of the 95 confidence interval for the true mean repair cost using the data provided (You may need one of the following cutoff values z 0 05 1 645, t 4,0 025 2 776, z 0 025 1 96, z 4,0 05 2 132) In order to use the method in part (c), do any assumptions need to be made If so, what are they What is the precision of the confidence interval constructed in part (c) 2 Briefly explain what the concepts of population and sample are in a statistical problem, how the two are related , and their relevance to the statistical analysis (One paragraph should suffice) 3 The average of a list of ten numbers is 100 and the standard deviation is 40 The smallest number in the list, 50, is deleted from the list Is it possible to determine what the average is for the remaining nine observations or is more information needed If so, what is the value of the average for the remaining nine observations If not, what additional information is needed (1 paragraph)

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Please solve with all information/text required. 1. BMW wishes to ascertain the mean repair costs for its cars in head-on collisions at 25 mph. In

Please solve with all information/text required.

1. BMW wishes to ascertain the mean repair costs for its cars in head-on collisions at 25 mph. In crash tests, only small samples are feasible so BMW decides to crash only five of its cars under the stated conditions. The repair costs (in dollars) are:

797 571 904 1147 418

Find the average cost of the five crashes.
Find the standard deviation of the cost for the five crashes.
Using the above data, BMW wishes to obtain a range of values that will encompass the true mean repair cost. Since they wish to use this for advertising purposes, they need to be nearly certain, in particular, 95% certain, the range of value will encompass the true mean repair cost. Consequently, they need to construct a 95% confidence interval for the true mean repair cost. Towards, this end, carry out the construction of the 95% confidence interval for the true mean repair cost using the data provided. (You may need one of the following cutoff values z_0.05 = 1.645, t_4,0.025 = 2.776, z_0.025 = 1.96, z_4,0.05 = 2.132)
In order to use the method in part (c), do any assumptions need to be made? If so, what are they?
What is the precision of the confidence interval constructed in part (c)?

2. Briefly explain what the concepts of population and sample are in a statistical problem, how the two are related, and their relevance to the statistical analysis. (One paragraph should suffice).

3. The average of a list of ten numbers is 100 and the standard deviation is 40. The smallest number in the list, 50, is deleted from the list. Is it possible to determine what the average is for the remaining nine observations or is more information needed? If so, what is the value of the average for the remaining nine observations? If not, what additional information is needed? (1 paragraph)