CI on Variance Defective alternator and corroded or loose battery charges are a few of the main causes of battery degradation. A company producing automobile batteries is developing a prototype on their next product and that they claim their batteries will last on average, 3 years with a variance of 1 year. A random sample of 5 prototype batteries were taken and in the course of the company's product development, have measured their lifetimes as 1.9, 2.4, 3.0, 3.5, and 4.2 years. Construct a 95% confidence interval for o? and decide if the company’s claim that o² = 1 is valid. Assume the population of battery lives to be approximately normally distributed. a. 0.34 < o2 < 4.59. Because 95% confidence interval for o? is (0.34, 4.59), and the s2 is in that interval, we can conclude that the company's claim is valid = 0.815 O b. 0.29 < o² < 6.74. Because 95% confidence interval for o² is (0.29, 6.74), and 1 is in that interval, we can conclude that the company's claim that ơ² = 1 is valid O c. 0.29 < o² < 6.74. 95% confidence interval for o² is (0.29, 6.74) O d. 0.539 < o< 2.596. Because 95% confidence interval for o is (0.539, 2.596), and 1 is in that interval, we can conclude that the company's claim that ơ = 1 is valid

Two groups of mice were injected with a measured amount of tumor pulp. The first group of 27 mice was given a high dosage of chemotherapy while the second group of 30 mice was given a low dosage of chemotherapy. After forty days, the first group had an average tumor size of 0.51cc with a variance of 0.10; the second group had an average tumor size of 0.64cc with a variance of 0.045. Were the tumor sizes of group 1 significantly smaller than those of group 2? What is the observed test statistic?

The average duration of labor from the first contraction to the birth of the baby in women over 35 who have not previously given birth and who did not use any pharmaceuticals is 16 hours. Suppose you have a sample of 35 women who exercise daily, and who have an average duration of labor of 16.9 hours and a sample variance of 39.7 hours. You want to test the hypothesis that women who exercise daily have a different duration of labor than all women. Calculate the t statistic. To do this, you first need to calculate the estimated standard error. The estimated standard error is SM = The t statistic is Now suppose you have a larger sample size n = 89. Calculate the estimated standard error and thet statistic for this sample with the same sample average and the same standard deviation as above, but with the larger sample size. The new estimated standard error is The new t statistic is Note that the t statistic becomes as n becomes larger. Use the Distributions tool to look at thet…

The average age at which adolescent girls reach their adult height is 16 years. Suppose you have a sample of 29 adolescent girls who are developmentally delayed, and who have an average age at which they reached their adult height of 17.8 years and a sample variance of 77.4 years. You want to test the hypothesis that adolescent girls who are developmentally delayed have a different age at which they reached their adult height than all adolescent girls. In order to calculate the t statistic, you first need to calculate the estimated standard error. The estimated standard error SM = (round to four decimals)

The average age at which adolescent girls reach their adult height is 16 years. Suppose you have a sample of 29 adolescent girls who are developmentally delayed, and who have an average age at which they reached their adult height of 17.8 years and a sample variance of 77.4 years. You want to test the hypothesis that adolescent girls who are developmentally delayed have a different age at which they reached their adult height than all adolescent girls. In order to calculate the t statistic, you first need to calculate the estimated standard error. The estimated standard error SM= (round to four decimals)

The fan blades on commercial jet engines must be replaced when wear on these parts indicates too much variability to pass inspection. If a single fan blade broke during operation, it could severely endanger a flight. A large engine contains thousands of fan blades, and safety regulations require that variability measurements on the population of all blades not exceed ?2 = 0.18 mm2. An engine inspector took a random sample of 81 fan blades from an engine. She measured each blade and found a sample variance of 0.28 mm2. Using a 0.01 level of significance, is the inspector justified in claiming that all the engine fan blades must be replaced? (b) Find the value of the chi-square statistic for the sample. (Round your answer to two decimal places.) Find or estimate the P-value of the sample test statistic. P-value > 0.1000.050 < P-value < 0.100    0.025 < P-value < 0.0500.010 < P-value < 0.0250.005 < P-value < 0.010P-value < 0.00 Find a 90% confidence interval…

The mean age of 31 slot mechanic player is 51.3 years, and the standard deviation is 6.8 years.the mean age of a different sample of 35 roulette player is 54.8 year and standard deviation is 3.2 years. Can it be concluded at alpha = 0.01 that the mean age of slot machine players is less than those players roulette? Assume the variance are equal Step 1= Step 2= Step 3= Step 4=

The variability in the amounts of impurities present in a batch of chemical used for a particular process depends on the length of time the process is in operation. A manufacturer using two production lines, 1 and 2, has made a slight adjustment to line 2, hoping to reduce the variability as well as the average amount of impurities in the chemical. Samples of 25 and 25 measurements from the two batches yield 1.04, respectively 0.51 variances. Do the data present sufficient evidence to indicate that the process variability is less for line 2? Use 5% significance level. Conduct a hypothesis test of the airline executive’s belief. [α = 0.05]

Diabetes Physicians recommend that children with type-I (insulin dependent) diabetes keep up with their insulin shots to minimize the chance of long-term complications. In addition, some diabetes researchers have observed that growth rate of weight during adolescence among diabetic patients is affected by level of compliance with insulin therapy. Suppose 12-year-old type-I diabetic boys who comply with their insulin shots have a weight gain over 1 year that is normally distributed, with mean = 13 lbs and variance = 13 lbs. (Assume for parts (a) and (b) that weight can be measured exactly and no continuity correction is necessary. Round your answers to four decimal places.) USE SALT (a) What is the probability that compliant type-I diabetic 12 year-old boys will gain at least 17 lbs over 1 year? X (b) Conversely, 12-year-old type-I diabetic boys who do not take their insulin shots have a weight gain over 1 year that normally distributed with mean = 7 lbs and variance = 13 lbs. Answer…