Week 6: Thursday MOM Homework Assignment Hypothesis Testing with One Sample Name: Vanessa Russell Exercises are set up so you can try the problem twice, then the answer will be shown on your third attempt. If you miss a problem on the exercises and want to improve your score, you can "Try a similar problem", which will give you a new question of the same type. You can keep on working on versions of a question until you get a perfect score on the exercises. #1 Points possible: 2. Total attempts: 3 You wish to test the following claim (H ) at a significance level of a H H = 0.02 . 69.4 o : = 69.4 a : You believe the population is normally distributed and you know the standard deviation is obtain a sample mean of M = 72.7 for a sample of size n = 19. = 6.9 . You What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic = What is the pvalue for this sample? (Report answer accurate to four decimal places.) pvalue = The pvalue is... less than (or equal to) greater than This test statistic leads to a decision to... reject the null accept the null fail to reject the null As such, the final conclusion is that... There is sufficient evidence to warrant rejection of the claim that the population mean is not equal to 69.4. There is not sufficient evidence to warrant rejection of the claim that the population mean is not equal to 69.4. The sample data support the claim that the population mean is not equal to 69.4. There is not sufficient sample evidence to support the claim that the population mean is not equal to 69.4. #2 Points possible: 2. Total attempts: 3 Test the claim that the mean GPA of night students is significantly different than 2.7 at the 0.2 significance level. The null and alternative hypothesis would be: H0 : p 0.675 H1 : p > 0.675 H0 : p 0.675 H1 : p < 0.675 H0 : 2.7 H1 : > 2.7 H0 : = 2.7 H1 : 2.7 H0 : 2.7 H1 : < 2.7 H0 : p = 0.675 H1 : p 0.675 The test is: twotailed lefttailed righttailed Based on a sample of 55 people, the sample mean GPA was 2.68 with a standard deviation of 0.05 The pvalue is: (to 2 decimals) Based on this we: Fail to reject the null hypothesis Reject the null hypothesis #3 Points possible: 2. Total attempts: 3 A poll done for Newsweek found that 16% of Americans have seen or sensed the presence of an angel. A contingent doubts that the percent is really that high. It conducts its own survey. Out of 76 Americans surveyed, only two had seen or sensed the presence of an angel. Is the contingent testing a mean or a proportion? mean proportion The alternate hypothesis, in symbols, is p' = > < 0.16. Suppose the contingent rejects the claim based on their survey. What type of error could they be making? Type I Type II #4 Points possible: 2. Total attempts: 3 Test the claim that the proportion of people who own cats is significantly different than 10% at the 0.05 significance level. The null and alternative hypothesis would be: H0 : 0.1 H1 : > 0.1 H0 : p 0.1 H1 : p < 0.1 H0 : 0.1 H1 : < 0.1 H0 : = 0.1 H1 : 0.1 H0 : p = 0.1 H1 : p 0.1 The test is: lefttailed righttailed twotailed Based on a sample of 700 people, 18% owned cats The pvalue is: Based on this we: Fail to reject the null hypothesis Reject the null hypothesis (to 2 decimals) H0 : p 0.1 H1 : p > 0.1 #5 Points possible: 2. Total attempts: 3 The state of CT claims that the average time on death row is 15 years. A random survey of 75 death row inmates revealed that the average length of time on death row is 17.3 years with a standard deviation of 5.6 years. Conduct a hypothesis to test the state of CT's claim. What type of test should be run? ttest of a mean ztest of a proportion The alternative hypothesis indicates a twotailed test lefttailed test righttailed test Calculate the pvalue. What is the decision? We fail to reject the claim that the average time on death row is 15 years We reject the claim that the average time on death row is 15 years #6 Points possible: 2. Total attempts: 3 Proctor & Gamble claims that at least half the bars of Ivory soap they produce are 99.44% pure (or more pure) as advertised. Unilever, one of Proctor & Gamble's competitors, wishes to put this claim to the test. They sample the purity of 101 bars of Ivory soap. They find that 44 of them meet the 99.44% purity advertised. What type of test should be run? ztest of a proportion ttest of a mean The alternative hypothesis indicates a righttailed test lefttailed test twotailed test Calculate the pvalue. Does Unilever have sufficient evidence to reject Proctor & Gamble's claim? No Yes