A random sample of 130130 observations produced a mean of ?=30.2x¯=30.2 from a population with a normal distribution and a standard deviation ?=4.49σ=4.49. (a) Find a 9999% confidence interval for ?μ
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A random sample of 130130 observations produced a
(a) Find a 9999% confidence interval for ?μ
Given:
Sample Mean (x̄) = 30.2
Standard Deviation (σ) = 4.49
Sample Size (n) = 130
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- Currently patrons at the library speak at an average of 68 decibels. Will this average decline after the installation of a new computer plug in station? After the plug in station was built, the librarian randomly recorded 60 people speaking at the library. Their average decibel level was 63.5 and their standard deviation was 15. What can be concluded at the the αα = 0.05 level of significance?The null and alternative hypotheses would be: H0:H0: Mean = __?__orrect H1:H1: Mean < __?__orrectC The test statistic t= __?__ (please show your answer to 3 decimal places.) The p-value = __?__ (Please show your answer to 4 decimal places.)Currently patrons at the library speak at an average of 64 decibels. Will this average change after the installation of a new computer plug in station? After the plug in station was built, the librarian randomly recorded 69 people speaking at the library. Their average decibel level was 61.7 and their standard deviation was 6. What can be concluded at the α = 0.05 level of significance? H0:H0: ? μ p Select an answer > ≠ < = H1:H1: ? p μ Select an answer = > < ≠ The test statistic ? t z = (please show your answer to 3 decimal places.) The p-value = (Please show your answer to 4 decimal places.)The mean number of sick days taken by employees in a year is 6. Members of the Human Resources department believe that employees take more than 6 sick days. A random sample of 52 employees had a mean of 6.42 sick days with a standard deviation of 1.6 days. Test the group’s claim at α = 0.05. (a) Write the null and alternative hypotheses. (b) Find the test statistic, t0. (write the answer as a decimal rounded to 4 decimal places) (c) Approximate the P-value. (write the answer as a decimal rounded to 4 decimal places)
- Scores on an IQ test are normally distributed. A sample of 25 IQ scores had variance of 64. The developer of the test claims that the population standard deviation is 15. Do these data provide sufficient evidence to significance? Use α=0.05α=0.05 . Answer the following questions. (a) What is the parameter? . (input as "mean", "standard deviation", "variance" or "proportion") (b) Determine if the alternative hypothesis is "right", "left" or "two-tailed" test. (input as "right", "left" or "two-tailed") (c) Test by using a confidence interval. Round confidence interval to nearest thousandth. (e.g. 0.1345 would be entered as 0.135) between ( and ) (d) State conclusion.: There is (input as "sufficient" or "insufficient") to (input as "conclude" or "reject") to conclude that the population standard deviation of IQ test is 15.You are a researcher studying the lifespan of a certain species of bacteria. A preliminary sample of 40 bacteria reveals a sample mean of ¯x=64x¯=64 hours with a standard deviation of s=4.2s=4.2 hours. You would like to estimate the mean lifespan for this species of bacteria to within a margin of error of 0.4 hours at a 95% level of confidence. What sample size should you gather to achieve a 0.4 hour margin of error? Round your answer up to the nearest whole number.You are a researcher studying the lifespan of a certain species of bacteria. A preliminary sample of 35 bacteria reveals a sample mean of ¯x=74x¯=74 hours with a standard deviation of s=4.2s=4.2 hours. You would like to estimate the mean lifespan for this species of bacteria to within a margin of error of 0.4 hours at a 95% level of confidence. What sample size should you gather to achieve a 0.4 hour margin of error? Round your answer up to the nearest whole number.
- You are a researcher studying the lifespan of a certain species of bacteria. A preliminary sample of 30 bacteria reveals a sample mean of ¯x=66x¯=66hours with a standard deviation of s=5.4s=5.4hours. You would like to estimate the mean lifespan for this species of bacteria to within a margin of error of 0.75 hours at a 99% level of confidence.What sample size should you gather to achieve a 0.75 hour margin of error? Round your answer up to the nearest whole number.n = bacteriaAn obstetrician read that a newborn baby loses on average 7 ounces in the first two days of his or her life. He feels that in the hospital where he works, the average weight loss of a newborn baby is less than 7 ounces. A random sample of 30 newborn babies has a mean weight loss of 6.4 ounces. The population standard deviation is 1.6 ounces. Is there enough evidence at =α0.01 to support his claim? Assume that the variable is normally distributed. Use the critical value method with tables. hello the question askas to find the critical value compute the test value and select the hypothesisA sample of 126 was found to have a standard deviation of 5.9. An interval estimate for ?μ based on the sample was (27.576, 29.464). What is the margin of error from this estimate? What was the ??,?tν,α that was used to get this interval extimate?
- You are a researcher studying the lifespan of a certain species of bacteria. A preliminary sample of 35 bacteria reveals a sample mean of ¯x=78x¯=78 hours with a standard deviation of s=5.6s=5.6 hours. You would like to estimate the mean lifespan for this species of bacteria to within a margin of error of 0.5 hours at a 95% level of confidence. What sample size should you gather to achieve a 0.5 hour margin of error? Round your answer up to the nearest whole number.You are a researcher studying the lifespan of a certain species of bacteria. A preliminary sample of 40 bacteria reveals a sample mean of ¯x=78x¯=78 hours with a standard deviation of s=4.4s=4.4 hours. You would like to estimate the mean lifespan for this species of bacteria to within a margin of error of 0.45 hours at a 99% level of confidence. What sample size should you gather to achieve a 0.45 hour margin of error? Round your answer up to the nearest whole number. n = bacteriaA sample of 55 measurements resulted in a sample mean, ?⎯⎯⎯=9.3x¯=9.3 and sample standard deviation ?=1.47s=1.47. Using ?=0.05α=0.05, test the null hypothesis that the mean of the population is 10.510.5 or less against the alternative hypothesis that the mean of the population, ?>10.5μ>10.5 by giving the following:(a) the degree of freedom (b) the test statistic The final conclusion is A. There is not sufficient evidence to reject the null hypothesis that ?=10.5μ=10.5. B. We can reject the null hypothesis that ?=10.5μ=10.5
