Math 1115 Assignment 3-Due date July 15th 1. [10 marks] Since 2007, the American Psychological Association has reported an annual nationwide survey to examine stress across the United States. A total of 340 Millennials were asked to indicate their average stress level (on a 10 point scale) during the past month. The mean score was 5.4. Assume that the population standard deviation is 2.3. a) Give the margin of error and find the 95% confidence interval for this sample. b) Repeat these calculations for a 99% confidence interval. How do the results compare with those in part (a)? H 0 : =0 2. [10 marks] A test of the null hypothesis gives test statistic z=1.77 a) What is the P-value if the alternative hypothesis is H a : > 0 ? b) What is the P-value if the alternative hypothesis is H a : < 0 ? c) What is the P-value if the alternative hypothesis is H a : 0 ? 3. [10 marks] There is a score from 0 to 200 for a test (SSHA). The mean score for college students is about 115, and the standard deviation is about 30. A teacher, who suspects that older students have better mark, gives SSHA to 25 students who are at least 30 years of age. Their mean score is x =127.8 . Assuming that =30 for the population of older students, carry out a test of H 0 : =115 H a : > 115 Report the P-value of your test, and state your conclusion. 4. [10 marks] According to data from the Tobacco Institution Testing Laboratory, Camel Light king size cigarettes contain an average of 0.61 milligrams of nicotine. An advocacy group commissions an independent test to see if the mean nicotine content is higher than the industry laboratory claims. H 0H a a) What are ? b) Suppose that the test statistic is z=1.72. Is this result significant at the 5% level? c) Is the result significant at the 1% level? 5. [20 marks] Consider the following situation: H 0 : =286 H a : 286 n=100 and =115 a) Given =0.05 , for what values of z will you reject the null hypothesis? b) Using =115 and =286 , for what values of x will you reject c) Using =115 and =271 , what is the probability that H0 ? x will fall in the region defined in part (b)? d) Will a sample size of n=100 give you adequate power? Or do you need to find ways to increase the power? Explain your answer. 6. [10 marks] The one-sample t statistic for testing H 0 : =40 H a : 40 From a sample of n=27 observations has the value t=2.01 a) What are the degrees of freedom for t? b) Locate the two critical values t from the Table D that bracket t. c) Between what two values does the P-value of the test fall? d) Is the value t=2.01 statistically significant at the 5% level? At the 1% level? 7. [10 marks] Researchers were interested in comparing the long-term psychological effects of being on a high-carbohydrate, low-fat(LF) diet versus a high-fat, low-carbohydrate (LC) diet. A total of 106 over-weight and obese participants were randomly assigned to one of these energy-restricted diets. At 52 weeks, 32 LC dieters and 33 LF dieters remained. Mood was assessed using a total mood disturbance score (TMDS), where a lower score is associated with a less negative mood. A summary of these results follows: Group n x s LC LF 32 33 47.3 19.3 28.3 25.8 a) Is there a difference in the TMDS at week 52? Test the null hypothesis that the dieters' average mood in the two groups is the same. Use significance level of 5%? b) Critics of this study focus on the specific LC diet (that is, the science) and the dropout rate. Explain why the dropout rate is important to consider when drawing conclusions from this study