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

A researcher studying the lifespan of a certain species of bacteria. A preliminary sample of 25 bacteria reveals a sample mean of ¯x=72x¯=72 hours with a standard deviation of s=5s=5 hours. He would like to estimate the mean lifespan for this species of bacteria to within a margin of error of 0.45 hours at a 90% level of confidence.What sample size should you gather to achieve a 0.45 hour margin of error?He would need to sample ________ bacteria. Fill in the blank.

Arsenic (chemical element) occurs naturally in some ground water. A mean arsenic level of μ = 7.0 per billion is (ppb) consider safe for agricultural use. A well in Texas is used to water cotton crops. This well is tested on a regular basis for arsenic. Test the claim that the arsenic in the ground water is more than 7.0 ppb.A random sample of 40 tests gave a sample mean of = x_bar = 7.5 ppb arsenic, with s = 1.9 ppb.  a. DF = 40, t-test statistic = 1.664, p-value = 0.0520 b. z-test statistic = 1.664, p-value = 0.0481 c. z-test statistic = 0.163, p-value = 0.4353 d. DF = 39, t-test statistic = 1.664, p-value = 0.0520

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…

Unfortunately, arsenic occurs naturally in some ground water†. A mean arsenic level of μ = 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 31 tests gave a sample mean of x = 6.9 ppb arsenic, with s = 2.5 ppb. Does this information indicate that the mean level of arsenic in this well is less than 8 ppb? Use ? = 0.05. What is the value of the sample test statistic? (Round your answer to three decimal places.) (c) Find the P-value. (Round your answer to four decimal places.)

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?

Unfortunately, arsenic occurs naturally in some ground water†. A mean arsenic level of μ = 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 31 tests gave a sample mean of x = 7.1 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 ? = 0.05. What is the level of significance? What is the value of the sample test statistic? (Round your answer to three decimal places.) Find the P-value. (Round your answer to four decimal places.)

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).