1 A salesperson created a 99% confidence interval of (205.16, 548.68) megabytes per month to estimate the average capacity usage of an iPhone. What is the value of the width of this confidence interval? Please give your answer correctly rounded to two decimal places and do NOT include units in your answer. 2 An electricity provider wants to estimate the mean time it takes for customers to get an electrical fault resolved. The provider took a random sample of 36 customers who had recently reported an electrical fault and found a mean time of 9.69 hours. Assume the population standard deviation is 0.55 hours. What is the value of the margin of error for a 95% confidence interval? Please give your answer correctly rounded to two decimal places and do NOT give units. 3 The production manager at a textile mill, believes that a new machine, producing cloth, is not working according to the company's specifications. The company requires that the cloth should have a mean breaking strength of 35 Kg. A sample of 60 pieces of cloth reveals a sample mean breaking strength of 40.5 Kg and a standard deviation of 0.7 Kg. If the manager wants to do a hypothesis test to her belief, what value of the mean would be used in the null and the alternative hypotheses? 4 Production managers, on an assembly line, must monitor the output to check if the level of defective products is greater than an average of 5 per production run. They continuously inspect a random sample of production runs and find the average number of defective parts produced. If they find a significant increase in the mean number of defective parts, they will stop the assembly line and fix the machinery. The hypotheses are: Ho: = 5 Ha: > 5 Say a random sample of 25 production runs is taken, where the mean number of defective parts is found to be 4.3 parts with a standard deviation of 0.5 parts. If testing at the 1% level of significance, what is the critical value? Please give your answer correctly rounded to two decimal place. 5 The following is information from a simple linear regression to estimate the energy content (calories) of a chocolate bar, based on the sugar content (grams) = 80.33+0.6 Sugar r = 0.82 n = 71 What is the value of the coefficient of determination? Please give your answer correctly rounded to two decimal places and do NOT create a percentage. 6 A lecturer wanted to investigate the relationship between a student's final mark (in points) for a subject and the number of hours the student studied in the trimester, outside of class time. They gathered a random sample of data and used EXCEL to create the following simple linear regression of marks on hours: SUMMARY OUTPUT Regression Statistics Multiple R 0.91 R Square 0.82 Standard Error 11.48 Observations 36 Coefficients Standard Error Intercept 3.82 4.5 Hours 0.76 0.13 Estimate the final mark for a student that studied a total of 10 hours outside of class time for this subject. Please give your answer correctly rounded to two decimal places and do NOT include units. 7 Due to the capacity of laptops, a market analyst believes that the number of laptops per household has increased. In the past, the mean number of laptops per household was 1.7 with a standard deviation of 0.2. To test his belief, the analyst takes a random sample of 56 households and finds a mean of 2.9 laptops. Let the significance level be 1%. Assume the conditions are satisfied. What is the value of the calculated test statistic? Please give your answer correctly rounded to two decimal place