Testing for the proportion of success HYPOTHESIS TESTING Testing for the proportion of success

SHORT TERM MEMORY A typical person can memorize a string of digits up to 7 numbers long Studies suggest that 90% of people can memorize a string of 7 digits. 40% of people can memorize a string of 9 digits. 20% of people can memorize a string of 11 digits.

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Testing of Hypothesis We would be interested in testing if a particular assumption regarding the population is true or not Null hypothesis – original assumption or statement that we wish to test. Alternative hypothesis Determine the critical value wherein we may reject our null hypothesis

Errors Type I Error - reject the null hypothesis when in fact it is true Probability α Type II Error - fail to reject the null hypothesis when in fact it is false Probability β Null Hypothesis is True Null Hypothesis is False Fail to Reject Correct Decision Type II Error (β) Reject Type I Error (α)

Steps in Hypothesis Testing Write the null and alternative hypothesis. Indicate the level of significance. Establish the critical regions and the rejection criterion. Compute the test statistic. Decide the conclusion of the test.

Hypothesis Testing for the Proportion Ho: p=pO H1: p≠pO, p>pO, p<pO Z-test will be used The test statistic is given by

Example 1 A commonly prescribed drug on the market for relieving nervous tension is believed to be only 60% effective. Experimental results with a new drug administered to a random sample of 100 adults who were suffering from nervous tension showed that 70 received relief. Is this sufficient evidence to conclude that the new drug is superior to the one commonly prescribed? Use a 0.05 level of significance.

Example 2 The Heldrich Center for Workforce Development found that 40% of Internet users received more than 10 e-mail messages per day. In 2001, a similar study on the use of e-mail was repeated. The purpose of the study was to see whether the use of e-mail had increased. If a sample of 420 Internet users found 188 receiving more than 10 e-mail messages per day, determine if the amount of e-mail received per day has increased. Use a 0.05 level of significance.

Example 3 Microsoft Outlook is believed to be the most widely used e-mail manager. A Microsoft executive claims that Microsoft Outlook is used by at least 75% of Internet users. A Merrill Lynch study reported that 216 out of 300 Internet users used Microsoft Outlook. Test if the Microsoft executive’s claim is true, against the alternative that less than 75% use Microsoft Outlook, using a 0.05 level of significance.

Example 4 Suppose that in the past, 40% of all adults favored capital punishment. Do we have reason to believe that the proportion of adults favoring capital punishment today has increased if, in a random sample of 150 adults, 87 favor capital punishment? Use a 0.05 level of significance.