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You have certainly heard the above claim before Advertisers frequently claim that some percentage of doctors or dentists recommend a given health product It s best to take such claims with a large grain of salt Suppose a recent advertisement claims that 9 out of 10 dentists 90 recommend a certain brand of toothpaste A consumer advocacy group is highly suspicious of this claim and randomly surveys 251 dentists They find that 92 6 of the sample recommends the given brand of toothpaste Using a 0 025 test the hypothesis that the proportion of all dentists who recommend this brand of toothpaste is different than 90 State the null and alternative hypothesis for this test Ho p V 0 9 H PV 0 9 Determine if this test is left tailed right tailed or two tailed two tailed O left tailed Oright tailed Should the standard normal 2 distribution or Student s t distribution be used for this test The Student s t distribution should be used The standard normal z distribution should be used Determine the critical value s for this hypothesis test Round the solution s to two decimal places If more than one critical value exists enter the solutions using a comma separated list 2 81 x Determine the test statistic Round the solution to two decimal places 1 3 X Determine the appropriate conclusion for this hypothesis test The sample data do not provide sufficient evidence to reject the null hypothesis that the proportion of all dentists that recommend this brand of toothpaste is 0 9 and thus we conclude that the proportion of dentists that recommend this brand of toothpaste is likely equal to 0 9 The sample data provide sufficient evidence to reject the null hypothesis that the proportion of all dentists that recommend this brand of toothpaste is 0 9 and thus we conclude that the proportion of dentists that recommend this brand of toothpaste is not equal to 0 9 The sample data do not provide sufficient evidence to reject the alternative hypothesis that the proportion of dentists who recommend this brand of toothpaste is significantly different than 0 9 and thus we conclude that the proportion of all dentists that recommend this brand of toothpaste is likely different than 0 9 The sample data provide sufficient evidence to reject the alternative hypothesis that the proportion of dentists who recommend this brand of toothpaste is significantly different than 0 9 and thus we conclude that the proportion of all dentists that recommend this brand of toothpaste is likely equal to 0 9

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