A sample of 8 measurements, randomly selected from a normally distributed population, resulted in a sample mean, = 9.3 and sample standard deviation s = 1.88. Using a = 0.01, test the null hypothesis that the mean of the population is 7.6 against the alternative hypothesis that the mean of the population, μ< 7.6 by giving the following: (a) the degree of freedom (b) the critical t value (c) the test statistic

Unfortunately, arsenic occurs naturally in some ground watert. A mean arsenic level of u = 8.0 parts per billion (ppb) is considered safe for agricultural use. A well in Texas is used to water cotton crops. This well is tested on a regular basis for arsenic. A random sample of 36 tests gave a sample mean of x = 7.0 ppb arsenic, with s = 2.3 ppb. Does this information indicate that the mean level of arsenic in this well is less than 8 ppb? Use a = 0.01. (a) What is the level of significance? State the null and alternate hypotheses. О но: и 3 8 рb; н,: и +8 ppb O Ho: H > 8 ppb; H: µ = 8 ppb O Ho: H = 8 ppb; H: µ > 8 ppb O Ho: H = 8 ppb; H,: µ < 8 ppb O Ho: H < 8 ppb; H,: µ = 8 ppb (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. O The standard normal, since the sample size is large and o is unknown. O The Student's t, since the sample size is large and o is unknown. O The standard normal, since the sample size is large and o is…

Unfortunately, arsenic occurs naturally in some ground watert. A mean arsenic level of u = 8.0 parts per billion (ppb) is considered safe for agricultural use. A well in Texas is used to water cotton crops. This well is tested on a regular basis for arsenic. A random sample of 41 tests gave a sample mean of x = 6.9 ppb arsenic, with s = 2.8 ppb. Does this information indicate that the mean level of arsenic in this well is less than 8 ppb? Use a = 0.05. (a) What is the level of significance? State the null and alternate hypotheses. О Но: и 8 pb О Но: и> 8 рpb; Hi: и %3D 8 рpb (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. O The Student's t, since the sample size is large and o is unknown. The standard normal, since the sample size is large and o is known. The Student's t, since the sample size is large and o is known. O The standard normal, since the sample size is large and o is unknown. What is the value of the sample test…

The admissions office at Memorial Hospital recently stated that the mean age of its patients was μ= 43 years with σ = 21.2 years. A random sample of 29 ages obtained from the admissions office records had a mean of 49.9 years. A hospital administrator doesn’t believe that a mean of 43 years is correct. Calculate the critical value AND answer does the evidence support the hospital’s claim (H_o) or the administrator’s claim (H_a) at the α = 0.05 level?

Use dataset "HT_4143.xls" and conduct a two-sample t-test using Excel. You'd like to test the null hypothesis that the means of the two samples (column A and column B) are the same. The alternative hypothesis is that they are not the same. You have no reason to believe that the standard deviations of the two samples are equal.  Test at the alpha = 0.10 level.   After using Excel, what do you conclude? Are the means the same? Group of answer choices You reject the null hypothesis. Therefore, you conclude that the means of the two populations are different. You reject the null hypothesis. Therefore, you conclude that the means of the two populations are the same. You cannot reject the null hypothesis. Therefore, you conclude that the means of the two populations are different. You cannot reject the null hypothesis. Therefore, you conclude that the means of the two populations are the same.   HT_ 4143.xls: X1          X299.73     98.6995.93     98.9494.92     96.63100.52   99.16101.28…

During a wisdom teeth removal procedure, 1, 2, 3, or 4 wisdom teeth are removed, depending on the patient's needs. Records indicate that nationwide, the mean number of wisdom teeth removed in a procedure is \mu = 3.10, with a standard deviation of \sigma = 1.06. Suppose that we will take a random sample of 10 wisdom teeth removal procedures and record the number of wisdom teeth removed in each procedure. Let x represent the sample mean of the 10 procedures. Consider the sampling distribution of the sample mean x. Complete the following. Do not round any intermediate computations. Write your answers with two decimal places, rounding if needed. (a) Find \mu_x (the mean of the sampling distribution of the sample mean). (b) Find \sigmax (the standard deviation of the sampling distribution of the sample mean).

A researcher studying the lifespan of a certain species of bacteria. A preliminary sample of 25 bacteria reveals a sample mean of = 70 hours with a standard deviation of s = 7 hours. He would like to estimate the mean lifespan for this species of bacteria to within a margin of error of 0.5 hours at a 99% level of confidence. What sample size should you gather to achieve a 0.5 hour margin of error? He would need to sample bacteria.

A soft drink bottler is interested in the smooth operation of the machine used to fill cans. In particular, you want the standard deviation of the filling process to be less than 0.2 fluid ounces; otherwise, there will be a higher than tolerable percentage of cans that will not be completely full.Assume that the fill volume is approximately normally distributed. A random sample of 20 cans results in a variance of S ^ 2 = 0.0225 (ounces) ^ 2. The image shows the creation of a 95% confidence interval Create an upper 95% confidence interval

Listed in the data table are amounts of strontium-90 (in millibecquerels, or mBq, per gram of calcium) in a simple random sample of baby teeth obtained from residents in two cities. Assume that the two samples are independent simple random samples selected from normally distributed populations. Do not assume that the population standard deviations are equal. City_#1 City_#2 100 117 86 84 121 100 120 85 101 90 104 107 213 110 136 111 290 126 100 133 289 101 145 209 Use a 0.01 significance level to test the claim that the mean amount of strontium-90 from city #1 residents is greater than the mean amount from city #2 residents. The test statistic is The P-value State the conclusion for the test. a ) reject, There is sufficient evidence to support the claim that the mean amount of strontium-90 from city #1 residents is greater. b )reject, There is not sufficient evidence to support the claim that the mean amount of strontium-90 from city #1 residents is greater. c ) fail to reject,…

Suppose we have independent observations X1 and X2 from a distribution with mean u and standard deviation o. What is the variance of the mean of the two values: ^1T42? 2