4.) The percentage of titanium in an alloy used in aerospace castings is measured in 51 randomly selected parts. The sample standard deviation is s = 0.37. Construct a 95% two-sided confidence interval for the standard deviation.
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4.) The percentage of titanium in an alloy used in aerospace castings is measured in 51 randomly selected parts. The sample standard deviation is s = 0.37. Construct a 95% two-sided confidence interval for the standard deviation.
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- Traffic Highway planners investigated the relationshipbetween traffic Density (number of automobiles per mile)and the average Speed of the traffic on a moderately largecity thoroughfare. The data were collected at the samelocation at 10 different times over a span of 3 months.They found a mean traffic Density of 68.6 cars per mile(cpm) with standard deviation of 27.07 cpm. Overall, the cars’ average Speed was 26.38 mph, with standard devia-tion of 9.68 mph. These researchers found the regression line for these data to be Speed = 50.55 - 0.352 Density.a) What is the value of the correlation coefficientbetween Speed and Density?b) What percent of the variation in average Speed isexplained by traffic Density? c) Predict the average Speed of traffic on the thorough-fare when the traffic Density is 50 cpm. d) What is the value of the residual for a traffic Densityof 56 cpm with an observed Speed of 32.5 mph?e) The data set initially included the point Density =125 cpm, Speed = 55 mph. This…Suppose the mean height in inches of all 9th grade students at one high school is estimated. The population standard deviation is 5 inches. The heights of 8 randomly selected students are 63, 60, 74, 68, 60, 66, 72 and 61. x¯ = Margin of error at 99% confidence level = 99% confidence interval =Is there strong evidence of global warming? Let’s consider a small scale example, comparing how temperatures have changed in the US from 1968 to 2008. The daily high temperature reading on January 1 was collected in 1968 and 2008 for 51 randomly selected locations in the continental US. Then the difference between the two readings (temperature in 2008 - temperature in 1968) was calculated for each of the 51 different locations. The average of these 51 values was 1.1 degrees with a standard deviation of 4.9 degrees. We are interested in determining whether these data provide strong evidence of temperature warming in the continental US. (d) Calculate the test statistic and find the p-value. (e) What do you conclude? Interpret your conclusion in context. (f) Calculate a 90% confidence interval for the average difference between the temperature measurements between 1968 and 2008. Interpret this interval in context. (g) Does the confidence interval provide convincing evidence that the…
- Paint used to paint lines on roads must reflect enough light to be clearly visible at night. Researchers have 2 new types of paints they want to test paint type A and paint type B. For each paint type, they tested if there was statistical evidence the average reflectometer reading is greater than 35. To test each type of paint, they used 15 paint samples. Further, suppose the standard deviation is the same for both types of paints. The sample mean for paint type A was 39 and the sample mean for paint type B was 41.5. For both statistical tests, the significance level is set to .05.Which of the following is true? If they fail to reject the null hypothesis for paint type A we can conclude there is statistical evidence the average reflectometer for type A paint is 35. The p-value for the type B paint test is smaller. They rejected the null hypothesis for both paint types. Exactly two of the statements above are true. None are true.During the past year, the flight times between two cities was reported to have a population standard deviation of 20 minutes. What would the margin of error be if a sample of 64 was used for estimating the mean flight time between the two cities and with a confidence level of 95%2. There was a sample of 14 adult wild mountain lions who were caught and released in the San Andres Mountains. The average weight of the sample was 82.55 pounds with a sample standard deviation of 13.45 pounds. Find a 95% confidence interval for the population mean weight of all the wild mountain lions in the San Andres Mountains.
- A sports writer wished to see if a football filled with helium travels farther, on average, than a football filled with air. To test this, the writer used 18 adult male volunteers. These volunteers were randomly divided into two groups of nine men each. Group 1 kicked a football that was filled with helium to the recommended pressure. Group 2 kicked a football that was filled with air to the recommended pressure. The mean yardage for Group 1 was ?¯1=300 yards with a standard deviation of ?1=8 yards. The mean yardage for Group 2 was ?¯2=296 yards with a standard deviation of ?2=6 yards. Assume the two groups of kicks are independent. Let ?1 and ?2 represent the mean yardage we would observe for the entire population represented by the volunteers if all members of this population kicked, respectively, a helium‑filled football and an air‑filled football. Assuming two‑sample ? procedures are safe to use and using Option 1 for the degrees of freedom, a 90% confidence interval for ?1−?2 is:…Researchers from a certain country were interested in how characteristics of the spleen of residents in their tropical environment compare to those found elsewhere in the world. The researchers randomly sampled 91 males and 109 females in their country. The mean and standard deviation of the spleen lengths for the males were 10.9 cm and 0.9 cm, respectively, and those for the females were 9.8 cm and 1.1 cm, respectively. Determine a 95% confidence interval for the difference between mean spleen lengths of males and females in this country. Click here to view page 1 of the table of critical values of t. Click here to view page 2 of the table of critical values of t. Let population 1 be all males in the country and let population 2 be all females in the country. The 95% confidence interval for µ1 - 4½ is ( | D (Round to three decimal places as needed. Use ascending order.)The average entrance exam score of a random sample of 35 freshmen students is 89.66 with a standard deviation of 18.28. Construct a 96% confidence interval for the true mean score of the freshmen students.
