xi 3 12 6 20 14 yi 55 40 55 10 15 a. Estimate the standard deviation of y when x=8 (to 4 decimals). b. Develop a 95 confidence interval for the expected value of y when x=8(to 2 decimals). ( , ) c.Estimate the standard deviation of an individual value of y when x=8 (to 4 decimals). d. Develop a 95% prediction interval for y when x=8 (to 2 decimals).
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| xi | 3 | 12 | 6 | 20 | 14 | |
| yi | 55 | 40 | 55 | 10 | 15 |
a. Estimate the standard deviation of y when x=8 (to 4 decimals).
b. Develop a 95 confidence interval for the
( , )
c.Estimate the standard deviation of an individual value of y when x=8 (to 4 decimals).
d. Develop a 95% prediction interval for y when x=8 (to 2 decimals).
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- A scientist is studying the paramecium, a one-celled organism, under a microscope. There are 1500 paramecia in the slide he is studying, and the standard deviation of their lengths is 0.12mm. He views a sample of 30 paramecia and finds that the mean length of these 30 specimens is 0.25mm. Give the point estimate of the mean length of the entire paramecium population in the slide? (a) (b) Construct a 95% confidence interval for the mean length of the population. (c) State the maximum error for the estimate?From generation to generation, the mean age when smokers first start to smoke varies. However, the standard deviation of that age remains constant at around 2.1 years. A survey of 38 smokers of this generation was done to see if the mean starting age is at least 19. The sample mean was 18.1 with a sample standard deviation of 1.3. Do the data support the claim at the 5% level? (i) Alpha (Enter an exact number as an integer, fraction, or decimal.)? =A random sample of 16 adult male wolves from the Canadian Northwest Territories gave an average weight x1 = 97 lb with estimated sample standard deviation s1 = 6.3 lb. Another sample of 22 adult male wolves from Alaska gave an average weight x2 = 88 lb with estimated sample standard deviation s2 = 7.1 lb. (a) Let ?1 represent the population mean weight of adult male wolves from the Northwest Territories, and let ?2 represent the population mean weight of adult male wolves from Alaska. Find a 75% confidence interval for ?1 – ?2. (Round your answers to one decimal place.) lower limit upper limit (b) Examine the confidence interval and explain what it means in the context of this problem. Does the interval consist of numbers that are all positive? all negative? of different signs? At the 75% level of confidence, does it appear that the average weight of adult male wolves from the Northwest Territories is greater than that of the Alaska wolves? Because the interval…
- A random sample of 82 eighth grade students' scores on a national mathematics assessment test has a mean score of 286. This test result prompts a state school administrator to declare that the mean score for the state's eighth graders on this exam is more than 280. Assume that the population standard deviation is 38. At α = 0.05, is there enough evidence to support the administrator's claim? Complete parts (a) through (e). (a) Write the claim mathematically and identify Ho and H₂. Choose the correct answer below. O A. Ho: ≤280 (claim) H₂:μ>280 O D. Ho: μ≤280 Ha: μ> 280 (claim) B. Ho: μ280 OF. Ho: μ = 280 H₂: µ>280 (claim)A random sample of 82 eighth grade students' scores on a national mathematics assessment test has a mean score of 286. This test result prompts a state school administrator to declare that the mean score for the state's eighth graders on this exam is more than 280. Assume that the population standard deviation is 38. At α = 0.05, is there enough evidence to support the administrator's claim? Complete parts (a) through (e). (a) Write the claim mathematically and identify Ho and H₂. Choose the correct answer below. O A. Ho: μ≤280 (claim) H₂:μ>280 O D. Ho: μ≤280 Ha: μ> 280 (claim) O B. Ho: μ280 OF. Ho: μ = 280 Ha: μ>280 (claim)A random sample of 87 eighth grade students' scores on a national mathematics assessment test has a mean score of 293. This test result prompts a state school administrator to declare that the mean score for the state's eighth graders on this exam is more than 285. Assume that the population standard deviation is 31. At α=0.03, is there enough evidence to support the administrator's claim? Complete parts (a) through (e). (a) Write the claim mathematically and identify H0 and Ha. Choose the correct answer below. A. H0: μ<285 Ha: μ≥285 (claim) B. H0: μ=285 (claim) Ha: μ>285 C. H0: μ≤285 Ha: μ>285 (claim) D. H0: μ=285 Ha: μ>285 (claim) E. H0: μ≥285 (claim) Ha: μ<285 F. H0: μ≤285 (claim) Ha: μ>285