5-1 Introduction 5-2 Inference on the Means of Two Populations, Variances Known Assumptions.

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5-1 Introduction

5-2 Inference on the Means of Two Populations, Variances Known Assumptions

The Sampling Distribution of is normally distributed if the (original) population distributions are normal, and is approximately normally distributed if the (original) population is not normal, but the sample size is large. Expected value of is The variance of is

5-2 Inference on the Means of Two Populations, Variances Known Hypothesis Testing on the Difference in Means, Variances Known

5-2 Inference on the Means of Two Populations, Variances Known Hypothesis Testing on the Difference in Means, Variances Known Discuss Example 5-1

5-2 Inference on the Means of Two Populations, Variances Known Type II Error and Choice of Sample Size in(5-2) should be

5-2 Inference on the Means of Two Populations, Variances Known Type II Error and Choice of Sample Size

5-2 Inference on the Means of Two Populations, Variances Known Type II Error and Choice of Sample Size Discuss Example 5-2

The OC curve can also be used to determine the probability of type II error. Calculate If, the probability of type II error is read off the OC curve corresponding to this value of n. If, the probability of type II error is read off the OC curve corresponding to If samples required are equal, it can also be determined while planning by the same procedure as before.

Example #5-2(p223) Two types of plastic are suitable for manufacturing an electronic component. The breaking strength is important. The company will not adopt plastic 1 unless its mean breaking strength exceeds that of plastic 2 by at least 10 psi. Sol: We conclude there is insufficient evidence to support the use of plastic 1 at  = 0.05.

Example #5-3(p223) Two burning rates of two different solid-fuel propellants used in aircrew escape systems are being studied. So, the mean burning rate is the parameter of interest. (a)Test that both propellants have the same mean burning rate. Reject the null hypothesis and conclude the mean burning rates do not differ significantly at  = 0.05.

(b) What is the P-value of the test in (a)? P-value =P( rejecting H0)= © What is the probability of type-II error if the true difference in mean burning rate is 2.5 cm/s?

Determine the required sample size for the situation in (b). If, from the table V(a), n=20. If, we need n=30.

5-2 Inference on the Means of Two Populations, Variances Known Confidence Interval on the Difference in Means, Variances Known

Example #5-3(d) The 95%CI on We are 95% confident that the mean burning rate for solid fuel propellant 2 exceeds that of propellant 1 by between 4.49 and 8.21 cm/s. Also, since the interval does not include 0, we can conclude that the mean burning rates of two propellants are significantly different.

5-2 Inference on the Means of Two Populations, Variances Known

5-2 Inference on the Means of Two Populations, Variances Known

5-2 Inference on the Means of Two Populations, Variances Known Confidence Interval on the Difference in Means, Variances Known Choice of Sample Size

Example #5-3 (d) Construct a 95% CI on the difference in means. We are 95% confident that the mean burning rate for solid fuel propellant 2 exceeds that of propellant 1 by between 4.49 and 8.21 m/s.

Example #5-7 What sample size would be required in each population if we wanted the error in estimating the difference in mean burning rate to be less than 4cm/s with 99% confidence? Sol: E=4 Take

Hw for , 5.8, 5.10