Find the value of ta/2 and n = 25 for the 90% confidence interval for the mean if the population standard deviation, ơ, is not known.
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- The mean score of a random sample of 22 students applicants who took the college entrance examination is calculated to be 76.9. The population standard deviation is known to be 27.4. Find the 99% confidence interval for the mean of the entire student applicant.A psychologist is studying smokers' self-images, which she measures by the self-image (SI) score from a personality inventory. For adults in the U.S., the mean SI score from this inventory is about 140 . The psychologist gathers a random sample of 12 SI scores of smokers and finds that their mean is 157 and their standard deviation is 34 . Assume that the population of SI scores of smokers is normally distributed with mean μ . Based on the sample, can the psychologist conclude that μ is different from 140 ? Use the 0.05 level of significance. Perform a two-tailed test. Then fill in the table below. Carry your intermediate computations to at least three decimal places and round your answers as specified in the table. The null hypothesis: H0: The alternative hypothesis: H1: The type of test statistic: (Choose one)ZtChi squareF The value of the test statistic:(Round to at least three decimal places.)…The heights of 9 men were taken with sample mean of 165 cm and standard deviation 5 cm. The heights of 7 Japanese women were taken with sample mean of 150 cm and standard deviation 3 cm. Assuming that the population standard deviations for heights of men and women are both the same, construct the 95% confidence interval for the difference in mean heights between men and women.
- A random sample of 40 students has mean annual earnings of $3120 and a standard deviation of $677.Construct the confidence interval for the population mean, u if c = 0.95.The newest model of a car battery from a popular brand is supposed to have a lifetime of 60 months, but the lifetime varies slightly from battery to battery. It is known that the population of all lifetimes (in months) of this model of car battery is approximately normally distributed. You are a product reviewer who wants to estimate the standard deviation for this population with a random sample of 22 car batteries. Follow the steps below to construct a 99% confidence interval for the population standard deviation of all lifetimes of this model of car battery. (If necessary, consult a list of formulas.) (a)Click on "Take Sample" to see the results from the random sample. Take Sample Number of carbatteries Sample mean Sample standard deviation Sample variance 22 57.16 0.38 0.1444 To find the confidence interval for the population standard deviation, first find the confidence interval for the population variance. Enter…The president of a large university wishes to compare the standard deviation of the ages of students presently enrolled to previous years. The distribution of ages has been approximately normal. Find the 90% confidence interval for the population standard deviation of the student ages of the University. A random sample of 20 university students has a standard deviation of 6.1 years in a mean of 23.8 years what is the confidence interval of the population standard deviation?
- The newest model of a car battery from a popular brand is supposed to have a lifetime of 60 months, but the lifetime varies slightly from battery to battery. It is known that the population of all lifetimes (in months) of this model of car battery is approximately normally distributed. You are a product reviewer who wants to estimate the standard deviation for this population with a random sample of 22 car batteries. Follow the steps below to construct a 99% confidence interval for the population standard deviation of all lifetimes of this model of car battery. (If necessary, consult a list of formulas.) (a)Click on "Take Sample" to see the results from the random sample. Take Sample Number of carbatteries Sample mean Sample standard deviation Sample variance To find the confidence interval for the population standard deviation, first find the confidence interval for the population variance. Enter the values…Many people believe that the average number of Facebook friends is 328. The population standard deviation is 32.2. A random sample of 60 high school students in a particular county revealed that the average number of Facebook friends was 340. At α = 0.05, is there sufficient evidence to conclude that the mean number of friends is greater than 328?Find the value of −zα/2 that corresponds to a confidence level of 89.48%.
- A nutritionist selected a random sample of n = 50 adult males. The average daily intake of dairy products was found to be x = 756 grams per day, with a standard deviation of s = 35 grams per day. Use this sample information to construct a 99% confidence interval for the mean daily intake of dairy products for adult men.A ecologist wishes to estimate the mean lifespan for a specific species of bird. Assume that bird lifespan is normally distributed and that each bird's lifespan is independent of all others. The researcher analyzes a random sample of n=7 deceased birds to find out how long they lived for. It is found that the mean lifespan in the sample is y= 5 4 years with standard deviation s=13 years. Choose the correct formula for a 95% confidence interval for the true mean lifespan. X± to.975,n O xt to.975,n-1 n-1 O none of these X+ Z0.975 O x+ to.975,n-1' O xt to.975,n-15