Degree of Certainty

Question

A company developing scanners to search for hidden weapons at airports has concluded that a new device is significantly better than the current scanner. The company made this decision based on a P-value of 0.03. Explain the meaning of the P-value in this context 

Two students studying BES I are worried about the failure rate. 

a) The first has no idea what the failure rate is so takes a random sample of 100 students of whom 28 failed. Based on the sample evidence, calculate the 95% confidence interval and interpret it. Would this student conclude that the failure rate is 20%? 

b) The second student has a prior belief that the fail rate is 20%. Set up and test the appropriate hypotheses, at a(alpha) =0.05 using the same sample as above. Would this student conclude that the fail rate is 20%? c) In your own words, compare your answers to part (a) and (b) above – do they reach the same conclusion? Why or why not?

Question

Using a chi-square goodness –of-fit test you can decide, with some degree of certainty, whether a variable is normally distributed. In all chi-square   tests for normality, the null and alternative hypotheses are as follows. Ho: The test scores have a normal distribution. Ha: The test scores do not have a normal distribution. Find the expected frequencies. Round to the nearest integer as needed. Class boundaries 49.5 – 58.5 58.5 – 67.5 67.5 – 76.5 76.5   – 85.5 85.5 – 94.5 Frequency, f 18 61 83 33 5 Expected frequency Determine   the Critical value, Xo2 = Calculate the test statistic X2 =