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Calculate the time for the colony to reach 1 million bacteria.
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- A researcher wants to know how long it takes, on average, for a certain species of bacteria to divide. She watches 17 cells through a microscope and times how long it takes them to divide. She obtains the following data, in hours:6.7, 10.5, 4.8, 5.2, 5.2, 10.6, 4.4, 5.7, 10.9, 7.5, 5.3, 4.4, 5.7, 5.2, 6.9, 4.5, 7.7Assuming the population standard deviation is σ=2σ=2, construct a 94% confidence interval for the average time it takes this species of bacteria to divide.xˉ=x̄=α2=α2=zα2=zα2=Margin of Error: E=E=We are 94% confident that this species of bacteria takes, on average, between hours and hours to divide.___A farmer would like to evaluate Miracle Grow when used on his potted daisy plants. He sets up 20 plants in a room all facing the same window, obtaining the same amount of sunlight, and waters them identically each day. For a month, he monitors how much each plant grows. Then, he adds Miracle Grow to every pot and monitors how much each plant grows during a month with Miracle Grow. At the end of two months, he discovers that 14 plants grew more with Miracle Grow. Test the hypothesis that Miracle Grow increases plant growth (using an alpha level of .01). a) Is this a one-tailed or two-tailed test? ( b) State the null hypothesis. c) State the alternative hypothesis. d) Find the critical value(s). e) Calculate the obtained statistic. f) Calculate the P-Value (significance) of the obtained statistic). g) Make a decision. h) What does your decision mean?Randomly drawing and immediately three red M&Ms in a row from a bag that contains 10 red M&Ms out of 30 M&Ms total
- Rasol RTPlPlease helpOn March 11, 2011, Japan suffered an earthquake and tsunami that caused a disastrous accident at the Fukushima nuclear power plant. Among many other results, amounts of iodine-131 that were 27 times the government limit were found in a sample of spinach 60 miles away.† Now, 27 times the government limit of iodine-131 is 54 thousand becquerels per kilogram.† The following table shows the amount I, in thousands of becquerels per kilogram, of iodine-131 that would remain after t days. t = time, in days I = amount ofiodine-131 0 54.00 1 49.52 2 45.41 3 41.64 4 38.18 (a) Show that the data are exponential. (In this part and the next, round to three decimal places.) Because t increases by 1 each time, to show that the data are exponential, we must show that the successive ratios (rounded to three decimal places) are the same. Because all of the ratios are equal to , the data are exponential. (b) Find an exponential model I that shows the amount of iodine-131…
- On March 11, 2011, Japan suffered an earthquake and tsunami that caused a disastrous accident at the Fukushima nuclear power plant. Among many other results, amounts of iodine-131 that were 27 times the government limit were found in a sample of spinach 60 miles away.† Now, 27 times the government limit of iodine-131 is 54 thousand becquerels per kilogram.The following table shows the amount I, in thousands of becquerels per kilogram, of iodine-131 that would remain after t days.A private opinion poll is engaged by a politician toestimate what proportion of her constituents favor thedecriminalization of certain minor narcotics violations.Use the formula of Exercise 12 to determine how large a sample the poll will have to take to be at least 95% con-fident that the sample proportion is off by less than 0.02.Equip male and female students with a small device that secretly records sound for a random 30 seconds during each 12.5-minute period over two days. Count the words each subject speaks during each recording period, and from this, estimate how many words per day each subject speaks. The published report includes a table summarizing six such studies.12 Here are two of the six: Readers are supposed to understand that, for example, the 56 women in the first study had x 16,177 and s 7520. It is commonly thought that women talk more than men. Does either of the two samples support this idea? For each study: (a) State hypotheses in terms of the population means for men (M) and women (F). (b) Find the two-sample t statistic. (c) What degrees of freedom does Option 2 use to get a conservative P-value? (d) Compare your value of t with the critical values in Table C. What can you say about the P-value of the test? (e) What do you conclude from the results of these two studies?
- A population of 200 healthy men was followed up for the development of prostate cancer. 10 men were followed-up for 1 year and were then lost to follow-up. After being followed-up for 5 years, 10 men developed prostate cancer. The remaining men who never developed prostate cancer were followed for 10 years. Calculate the total number of person years of observation accrued by this populationA city contains 300,000 people (140,000 males and 160,000 females), and 3,000 people die per year from all causes of death (1,200 males and 1,800 females). There were 150 cases of heart disease per year (100 males and 50 females), of which 135 died (102 males and 33 females). Compute the following. Cause-specific mortality rate for heart disease Case-fatality rate for heart disease Proportionate mortality ratio for hearBy intergration
