First Semester 1435‐1436H King Abdul Aziz University
Statistical Methods Course Faculty of Science
Stat 302 Department of statistics‐Girls Campus
2 Assignment
Name:………..
ID:………..
Section:………..
Marks:……….
The deadline : 2/1/1436 H (26/10/2014)
Answer the following questions:
1‐ The percentage of titanium in an alloy used in aerospace casting is measured in 51 randomly selected parts. The sample standard devia on is s=0.37.
a) Construct a 95% two sided confidence interval for σ .
b) Construct a 95% one sided (upper) confidence interval for σ .
2‐ The fraction of defective integrated circuits produced in a photolithography process is being studied. A random sample of 300 circuits is tested, revealing 13 defec ves.
a) Calculate a 95% two sided CI on the frac on of defec ve circuits produced by this particular tool.
b) Calculate a 95% upper confidence bound on the frac on of defec ve circuits
3‐ In a random sample of 85 automobile engine cranksha bearing, 10 have a surface finish that is rougher than the specifications allows. Find a two sided 95% confidence interval for P. ( P is the propor on of bearings in the population that exceeds the roughness specification)
4‐ A researcher wishes to estimate the proportion of executives who own a car phone. She wants to be 90% confident and be accurate within 5% of the true proportion. Find the minimum sample size necessary.
5‐ The life in hours of a battery is known to be approximately normally distributed, with standard devia on σ = 1.25 hours. A random sample of 10 batteries has a mean life of ̅ 40.5 hours.
a) Is there evidence to support the claim that ba ery life exceeds 40 hours?
Use α = 0.05.
b) What is the P‐value for the test in part (a).
6‐ For the hypothesis test : μ 7 against : μ 7 with variance unknown and n = 20, approximate the P‐value for each of the following test statistics a) 2.05 b) 1.84
7‐ A researcher reports the results of a study that measured the body weight (in grams) for animals at birth.
421 452.6 456.1 494.6 373.8 90.5 110.7 96.4 81.7 102.4 241 296 317 290.9 256.5 447.8 687.6 705.7 879 88.8 296 273 268 227.5 279.5 258.5 296
a) Test the hypothesis that mean body weight is 300 grams. Use α = 0.05
b) What is the smallest level of significance at which you would be willing to
reject the null hypothesis?
c) Explain how you could answer the question on part (a) with a two sided confidence interval on mean body weight.
8‐ The data from Medicine and Science in Sports and Exercise considered ice hockey player performance after electrostimulation training. In summary, there were 17 players and the sample standard devia on of performance was 0.09 seconds.
a) Is there strong evidence to conclude that the standard deviation of performance me exceeds the historical value of 0.75 seconds? Use α = 0.05. Find the P‐value for this test.
b) Discuss how part (a) could be answered by construc ng a 95% one sided confidence interval for σ
9‐ Suppose that 500 parts are tested in manufacturing and 10 are rejected a) Test the hypothesis : 0.03 against : 0.03 at α= 0.05. Find
the P‐ value
b) Explain how the question in part (a) could be answered by constructing a 95% one sided confidence interval for p
10‐ In a random sample of 85 automobile engine cranksha , 10 have a surface finish roughness that exceeds the specification. Does this data present strong evidence that the proportion of crankshaft bearing exhibiting exhibiting excess surface roughness exceeds 0.10 ? State and test the appropriate hypotheses using α = 0.05.
