5. Two different types of alloy, Alloy A and Alloy B, have been used to manufacture a small tension link in a particular engineering application. The ultimate strength (ksi) of each specimen selected at random and tested in the company lab provided the following table:
Strength(ksi)/Alloy A/Alloy B
26-30/ 6 /4
30-34/ 12 /9
34-38/ 15 /19
38-42/ 7 /10
a)Compute a 95% Confidence Interval for difference between the true proportion of all specimens of Alloy A and Alloy B that have an ultimate strength of at least 34 ksi.
b)Calculate the appropriate test statistic to test the hypothesis: there is no with an ultimate strength of at least 34 ksi, against the alternative hypothesis that there is a difference in the two proportions. Use a level of significance of 0.05.
c)What conclusion do you draw do you draw from the result of part b?2 個解答語言1 0 年前
1.Suppose that your waiting time for a bus to take you to work on any given workday morning is Uniformly distributed between [0,5] minutes, while your waiting time for a bus to take you home on any given workday evening is Uniformly distributed between [0,10] minutes and independent of the morning wait. If you take a bus to and from work, on each of five consecutive work days, answer the following questions.
a)Find the mean of your total waiting time for the week.
b)Find the variance of your total waiting time for the week
c)Find the mean and variance of the difference between morning and evening waiting times on a given day.
d)Find the mean and the variance of the difference between the total morning waiting time and the total evening waiting time for the week.
2. Tardive dyskenesia is a syndrome comprising a variety of involuntary movement assumed to follow long-term use of certain anti-psychotic drugs. In an experiment to see whether the drug Deanol produce a greater improvement in symptoms, than a placebo treatment, from baseline scores, the two treatments were administrated for four week each, in random order to each of 14 patient, resulting in the following severity improvement index scores:
Patient 1 2 3 4 5 6 7 8 9 10 11 12 13 14
Deanol 12.4 6.8 12.6 13.2 12.4 7.6 12.1 5.9 12 1.1 11.5 13 5.1 9.6
Placebo 9.2 10.2 12.2 12.6 12.1 9 12.4 5.9 8.5 4.8 7.8 9.1 3.5 6.4
a)State the appropriate null and alternative hypothesis for this situation. Use a level of significance of 0.05.
b)Test the hypothesis of part a with an appropriate test statistic and state your conclusion.2 個解答語言1 0 年前