1- As a store manger you would like to find out the average time it takes to unload the truck which delivers the merchandise for your store. For this purpose, you have taken a random sample of 35 days and found the average unload time to be 263 minutes for the sample. You also found that the standard deviation is 45 minutes for the sample. Find the upper boundary of the 95% confidence interval for the average unload time. Round the answer to two decimal places. 2- For the standard normal distribution, compute two decimal places. 3- A poll is to be conducted to find out how many books, on average, Canadians read. You are the person who is to select a random sample and to ask the people of the sample about the number of books they read in the previous year. How many people are needed for your sample to estimate the number of books within 2 books with 90% confidence? Assume that it is known that the standard deviation for number of books read by Canadians is 11.7 books. 4- It is known that the average return on a stock is 28.2% with the standard deviation equal to 23.6%. A simple random sample of 68 returns is to be selected and the average return of the sample is to be found. You can say that this sample average is a random variable. What is the standard deviation of this random variable? Round your answer to 2 decimal places. 5- For the Student's t-distribution with 15 degrees of freedom, compute and round the answer to two decimal places. 6- Consider the following test performed with the level of significance 0.05: . Use Excel and round the answer to . Use Excel A random sample of size 40 is obtained from a normally distributed population. The population standard deviation is equal to 22.3. The sample mean happened to be 102.5. For this hypothesis test, what will be the critical value (the relevant z-alpha)? Hint: Watch the sign - the critical value can be negative or positive. Round the answer to three decimal places. 7- What is the proportion of customers who buy service plans when they buy a computer? To find out, you surveyed 146 customers and found that 48 purchased the service plan. What is the upper boundary of 90% confidence interval for the population proportion? Use Excel and round your answer to two decimal places. Give the answer as a decimal percent (that is, for 10%, give 0.1). 8- Consider the following test: A random sample of size 21 is obtained from a population that is known to be normally distributed with the population standard deviation equal to 11.2. If the sample mean happened to be 49, compute the test statistic. Round the answer to two decimal places. 9- Using Excel, find the right-tail probability corresponding to the following t value. Round the answer to 4 decimal places. t = 1.456. There are 7 degrees of freedom. 10- The best way to find out the average salary in your company is to perform a technique, known as Advanced Calibrated Sampling (ACS). This technique works in the following way: you must select a random sample of those employees, who have indicated that their salary is above $50,000 and exclude those, who indicated their salary to be above $100,000. Then you find the average salary of the selected employees. Agree Disagree 11- Consider the following test If the test statistic appears to be -2.34 and the critical value appears to be -2.3, should you accept the alternative hypothesis? 12- Yes No Based on the analysis of a random sample consisting of 45 months, 96% confidence interval for the average monthly profit is [$100,566; $111,457]. Explain in less than 100 words what this means. 13- A market research study in one Canadian city showed that the mean fare charged by taxi drivers is $21 and the standard deviation is $3.5. A random sample of 15 fares has been selected. What is the probability that the mean fare is between $20 and $23? Please type the solution and the answer. Use the formula editor to enter numeric values and formulas. This question will be marked manually by your professor. 14- In 2015, 56% of employed adults reported that mathematical skills were very important to their job. The supervisor of the job placement office at a college thinks that this percentage has increased due to increased use of technology in the workplace. She takes a random sample of 480 employed adults and finds that 297 of them feel that mathematical skills are very important to their job. Is there sufficient evidence to conclude that the percentage of employed adults who feel mathematical skills are very important to their job has increased at 0.05 level of significance? Please type the solution and the answer. Use the formula editor to enter numeric values and formulas. This question will be marked manually by your professor. 15- A probability distribution of all possible sample means is called the ------- distribution of the sample mean. Select true statements. There might be several true statements. Each correct answer gives a mark. In you select an answer incorrectly, a mark will be subtracted. Therefore, please do not guess. Note that this question cannot earn a negative mark - the lowest mark for this question is 0. A. The sampling distribution of the sample mean tends to become a bell-shaped distribution as the sample size increases. B. The standard deviation of the sampling distribution of the sample mean is bigger than the standard deviation of the population. C. The mean of all possible sample means of a given size is exactly equal to the population mean. D. The bigger the sample size, the bigger is the standard deviation of the sampling distribution of the sample mean. 16- 17- A manager, who works for your company, said at a business meeting: We have asked employees who would volunteer to participate in the survey. We paid $100 to each employee for the participation, to be fair and compensate for the time spent answering the survey questions. Because of this, the participation was high and we could achieve the sample size of 130. Based on this sample, we found that the confidence interval for the proportion of happy employees in our company is [97.6%, 99.2%], with the confidence level of 95%. Please note that we had to use the Student's t-distribution with 95 degrees of freedom to find this confidence interval. Thus, our analysis has shown that at least 97.6% of our company's employees are very happy. What is wrong with the manager's statement? Keep in mind that this question allows multiple correct answers and incorrect answers will result in the mark reduction. 1- Not mentioning other errors, the manager used the incorrect number of degrees of freedom. 2- The manager must have used 99% confidence level. 3- The sample size must have been bigger, because one cannot compute the confidence intervals with sample sizes with fewer than 150 items. 4- The manager used an incorrect probability distribution to find the confidence interval. 5- Even if the manager had computed the confidence interval correctly, the manager failed to draw the correct conclusion. The mentioned confidence interval does not mean that at least 97.6% of employees are happy. 66- The sample which the manager used was biased and therefore it could not be used for the statistical analysis