Question

1-4

1. State the null hypothesis, alternative hypothesis and identify the claim for each conjecture a. A medical researcher is interested in finding out whether a new medication will have undesirable effects on patients pulse rates. Since she knows that the mean pulse rate for the population under the study is 82 beats per minute, the hypotheses for this situation are: b. A contractor wishes to lower heating bills by using a special type of insulation in houses. If the average monthly heating bill is $278, her hypotheses for this situation are: c. A chemist invents an additive to increase the life of an automobile battery. If the mean lifetime of the automobile battery without the additive is 48 months, her hypotheses for this situation are: 2. Find the critical value(s) for each situation and draw the appropriate figure, showing the critical region. a. A right-tailed test with .05 b. A two-tailed test with α-01 c A left-tailed test with α·04 3. A researcher claims that the average cost of men's athletic shoes is less than $80. He selects a random sample of 36 pairs of shoes from a catalog and finds the following cost (in dollars- rounded to the nearest dollar). Is there enough evidence to support the researcher's claim at α .107 Assume that σ 19.2 60 70 75 55 80 55 50 40 80 70 50 95 20 90 75 85 80 60 110 65 80 85 85 45 75 60 90 90 60 95 110 85 45 90 70 70 4. An educator claims that the average salary of substitute teachers in school district in Allegheny County, Pennsylvania, is less than $60 per day. A random sample of eight school districts is selected, and the daily salaries (in dollars) are shown. Is there enough evidence to support the educator's claim at α-.10? 60 5660 55 70 55 60 55

Answer 1

1:

(a)

Here test should be two tailed. Hypotheses are:

Ho : μ = 82

$H_{a}:\mu\neq 82\text{ (claim)}$

(b)

Here test should be left tailed. Hypotheses are:

$H_{0}:\mu=278$

Ha : μ < 278 (claim)

(c)

Here test should be right tailed. Hypotheses are:

$H_{0}:\mu=48$

$H_{a}:\mu>48 \text{ (claim)}$