Questions:

1.State whether the following are true or false and give a brief explanation.

i. It is possible for the range of a data set to be the same as the inter-quartile range.

ii. If A and B are mutually exclusive events with positive probabilities, then A and B are independent.

iii. If the p value of a hypothesis test is 0.04, then the null hypothesis is rejected at 5% significance level.

iv. If the correlation coefficient between an independent variable x and a dependent variable y is positive, then it is possible for the slope of the estimated regression equation b to be negative.

v. For a confidence interval estimation of population mean , we use t distribution if the sample size is small.

2.A manufacturer supplies the rear axles for trucks. These axles must be able to withstand 80,000 pounds per square inch in stress tests, but an excessively strong axle raises production costs significantly. Long experience indicates that the standard deviation of the strength of its axles is 4,000 pounds per square inch. The manufacturer selects a sample of 100 axles from production, tests them, and finds that the mean stress capacity of the sample is 79,600 pounds per square inch. The axle manufacturer would like to know whether the axles meet his stress requirements.

(i) State the null and alternative hypothesis.

(ii) Find the value of the test statistic.

(iii) What is your conclusion at 10% significance level?

(iv) Find the p value of the test.