A manufacturer of sports equipment has developed a new synthetic fishing line that claims to have a mean breaking strength of 10kg with a standard deviation of 0.7kg. Test the hypothesis that p = 10kg against p # 10kg and find if a random sample of 55 lines is tested and found to have mean breaking strength of 8kg. Use 0.01 level of significance.
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- The mean age when smokers first start is 13 years old with a population standard deviation of 1.9 years. A researcher thinks that smoking age has significantly changed since the invention of ENDS- electronic nicotine delivery systems. A survey of smokers of this generation was done to see if the mean age has changed. The sample of 30 smokers found that their mean starting age was 12.2 years old. Do the data support the claim at the 1% significance level? What are the correct hypotheses? Ho: Select an answer v ? v years H3: Select an answer v years The test is: O One-tailed O Two-tailedAccording to a city's estimate, people on average arrive 1.5 hours early for domestic flights. The population standard deviation is known to be 0.5 hours. A researcher wanted to check if this is true so he took a random sample of 50 people taking domestic flights and found the mean time to be 2.0 hours early. At the 1% significance level, can you conclude that the amount of time people are early for domestic flights is more than what the city claims. Will you reject or not reject the null hypothesis and what is your conclusion in words? O Reject the null hypothesis; the city's claim is true. O Do not reject the null hypothesis; the city's claim is false and people arrive earlier than the city claims. O Reject the null hypothesis; the city's claim is false and people arrive earlier than the city claims. O Do not reject the null hypothesis; the city's claim is true.The owner of a local pizza store wishes to compare the sales per day at two different locations. The mean number of pizzas sold for 10 randomly selected days at Nizwa was 75.06 with a population standard deviation of 10.50. For a randomly selected 12 days at Muscat, the mean number of pizzas sold was 73.80 with a population standard deviation of 14.25. We wish to test whether there is a difference in the mean number of pizzas sold at the two locations using ?a 5 % significance level. What is the value of the test statistic in this case 1.71 .A O 1.84 .B None of these .C O 0.24 .D 2.20 .E O 2.65 .F O
- An interested citizen wanted to know if Democratic U. S. senators are older than Republican U.S. senators, on average. On May 26 2013, the mean age of 30 randomly selected Republican Senators was 61 years 247 days old (61.675 years) with a standard deviation of 10.17 years. The mean age of 30 randomly selected Democratic senators was 61 years 257 days old (61.704 years) with a standard deviation of 9.55 years. Do the data indicate that Democratic senators are older than Republican senators, on average? Test at a 5% level of significance. a. At the 5% level of significance, from the sample data, there is NOT sufficient evidence to conclude that the mean age of Democratic senators is greater than the mean age of the Republican senators. b. At the 5% level of significance, from the sample data, there is sufficient evidence to conclude that the mean age of Democratic senators is greater than the mean age of the Republican senators.In a one-way analysis of variance with three treatments, each with five measurements, in which a completely randomized design is used, what is the degrees of freedom for treatments? a. 5 b. 2 c. 4 d. 8The Sunny Dale Bank monitors the time required to serve customers at the drive-through window because it is an important quality factor in competing with other banks in the city. After analyzing the data gathered in an extensive study of the window operation, bank management determined that the mean time to process a customer at the peak demand period is 5 minutes, with a standard deviation of 1.5 minutes. Management wants to monitor the mean time to process a customer by periodically using a sample size of six customers. Assume that the process variability is in statistical control. Design an x-chart that has a type I error of 5 percent. That is, set the control limits so that there is a 2.5 percent chance a sample result will fall below the LCL and a 2.5 percent chance that a sample result will fall above the UCL. After several weeks of sampling, two successive samples came in at 3.70 and 3.68 minutes, respectively. Is the customer service process in statistical control?
- A sample of 45 adult men from Lahug showed that the mean time they spend working from home is 28.50 hours per week with a standard deviation of 4 hours. Another sample of 40 adult men from Pardo showed that the mean time spent by them working from home is 23.25 hours per week with a standard deviation of 5 hours. Using a 2.5% significance level, can you conclude that the mean time spent working from home by adult men in Lahug is greater than that for adult men in Pardo? Assume that the standard deviations for the two populations are equal.Bone mineral density (BMD) is a measure of bone strength. Studies show that BMD declines after age 45. The impact of exercise may increase BMD. A random sample of 59 women between the ages of 41 and 45 with no major health problems were studied. The women were classified into one of two groups based upon their level of exercise activity: walking women and sedentary women. The 39 women who walked regularly had a mean BMD of 5.96 with a standard deviation of 1.22. The 20 women who are sedentary had a mean BMD of 4.41 with a standard deviation of 1.02. Which of the following inference procedures could be used to estimate the difference in the mean BMD for these two types of womenAn elementary school class ran 1 mile with a mean of 11 minutes and a standard deviation of 3minutes. Rachel, a student in the class, ran 1 mile in 8 minutes. A junior high school class ran 1mile with a mean of 9 minutes and a standard deviation of 2 minutes. Kenji, a student in the class,ran 1 mile in 8.5 minutes. A high school class ran 1 mile with a mean of 7 minutes and a standarddeviation of 4 minutes. Nedda, a student in the class, ran 1 mile in 8 minutes. a. Why is Kenji considered a better runner than Nedda, even though Nedda ran faster than he? b. Who is the fastest runner with respect to his or her class? Explain why
- Suppose the mean weight of King Penguins found in an Antarctic colony last year was 15.4 kg. In a sample of 35 penguins same time this year in the same colony, the mean penguin weight is 14.6 kg. Assume the population standard deviation is 2.5 kg. At .05 significance level, can we reject the null hypothesis that the mean penguin weight does not differ from last year? Use P-value approach.A research firm supplies manufacturers with estimates of the sales of their products from samples of stores. Marketing managers often look at the sales estimates and ignore sampling error. An SRS of 50 stores this month shows mean sales of 41 units of a particular appliance with standard deviation of 11 units. During the same month last year, an SRS of 52 stores gave mean sales of 38 units of the same appliance with a standard deviation of 13units. An increase from 38to 41 is a rise of 7.9%.. The marketing manager is happy because sales are up 7.9%. (a) Give a 95%confidence interval for the difference in mean number of units of the appliance sold at all retail stores. Give your answers to three decimal places. lower bound: upper bound:A blood bank is conducting a study on how much time is required of their patients for blood platelet donations. Based on past records, time spent in the waiting room has a mean of 5 minutes and a standard deviation of 1 minute, time spent with a nurse who reviews patients' medical records and measures their vital signs has a mean of 10 minutes and a standard deviation of 3 minutes, and the actual donation time has a mean of 130 minutes and a standard deviation of 8 minutes. Assuming these three times are independent and can all be modeled using a normal distribution, approximately what proportion of donors finish the entire donation process in under 2.5 hours (150 minutes)? (A) 0.66 (B) 0.72 (C) 0.84 (D) 0.89 (E) 0.99