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Describe the steps in the procedure for testing hypotheses. Discuss the difference between a null hypothesis and an alternative hypothesis.
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There are five steps in the procedure for testing hypothesis. One must first state the research problem in a manner that clearly defines what is to be tested as well as identifying variables in the data collection. The population of interest and the parameters must be identified. An example might be "14 to 20 year old males prefer Pepsi over Coke."
The first step is to specify the null and alternative hypothesis. The null hypothesis and alternative hypothesis are opposites of one another. If the hypothesis is "14 to 20 year old males prefer Pepsi over Coke," the null hypothesis is "14 to 20 year old males do not prefer Pepsi to Coke." A null hypothesis would reflect that "there is no observed effect for (the) experiment," (Taylor, 2014) or in other words, there is no correlation between 14 to 20 year old males and their preference for Pepsi over Coke. The mathematical formulation for a null hypothesis ...
This detailed solution explains the procedure for testing hypotheses. It also discusses the difference between a null hypothesis and an alternative hypothesis. Includes example and APA formatted references.
Hypothesis Testing: Null and Alternate Hypotheses, P Value
Four Hypothesis Testing problems
Problem 10.17: M&M/Mars claims that at least 20% of the M&M's in each package are the new blue color. Set up the null and alternate hypotheses to test this claim.
Problem 10.18: The computer center at a university claims that the average amount of time that students spend on-line has increased from last year's average of 1 hour per day. Set up the null and alternative hypotheses to test this claim.
Problem 10.20: Recent medical research indicates that skin cancer patients who receive a new medication for skin cancer live longer than those who do not. The average length of life prior to the development of this medication was 18 months. The medical community wishes to test the claim made by the developers of this drug. A sample of 35 patients who received the medication lived an average of 21 months. The standard deviation is 5 months.
a) Set up the null and the alternative hypotheses to test if average length of life has increased from 18 months.
b) Test your hypotheses using a = 0.05.
c) Find the p value.
d) Based on the p value, what can you conclude about the average length of life for patients who receive the vaccine?
Problem 10.22: A manufacturer of top-of-line tennis rackets claims that its Smack Em tennis racket will change a player's game. A tennis pro currently serves the ball at an average speed of 115 mph with a standard deviation of 2.5 mph. The speeds are normally distributed. The tennis pro decides to test the company's claim and records the speed of his serve for 15 balls using the Smack Em racket. The data are shown in the following table: Speed
a) Set up the null and the alternative hypotheses to test if the average service speed has increased using the new racket.
b) Test your hypotheses using a = 0.05
c) Find the p value.
d) Based on the p value, should the tennis pro invest in the new racket?