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=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 0.6 hours at a 95% level of confidence. What sample size should you gather to achieve a 0.6 hour margin of error? Round your answer up to the nearest whole number. n =   bacteria

A random sample of 76 eighth-grade​ students' scores on a national mathematics assessment test has a mean score of 273. 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 270. Assume that the population standard deviation is 33. At α=0.02​, is there enough evidence to support the​ administrator's claim? Complete parts​ (a) through​ (e). Part 1 ​(a) Write the claim mathematically and identify H0 and Ha. Choose the correct answer below.   A.) H0​: μ≥270 (claim)       Ha​: μ<270   B.) H0​: μ≤270 (claim)       Ha​: μ>270   C.) H0​: μ=270 (claim)       Ha​: μ>270   D.) H0​:μ≤270       Ha​: μ>270 ​(claim)   E.) H0​: μ<270       Ha​: μ≥270 ​(claim)   F.) H0​: μ=270      Ha​: μ>270 (claim)     (b) Find the standardized z, and its coresponding area      z=_____   (c) Find the P-value P-value =_____   (d) Decide whether to reject or fail the null…

A standardized memory test has a mean of μ = 100 and a standard deviation of σ= 10. What percent of individuals would score between 89 and 115?

A researcher studying the lifespan of a certain species of bacteria. A preliminary sample of 30 bacteria reveals a sample mean of ¯x=68x¯=68 hours with a standard deviation of s=7s=7 hours. He 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?He would need to sample  bacteria.