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 sample of n=4 scores had EX=8 and EX^2=40. Ehat is the value of the sample variance s^2

Unfortunately, arsenic occurs naturally in some ground water. A mean arsenic level of u = 8 parts per billion (ppb) is considered safe for agricultural use. A well in Los Banos is used to water cotton crops. This well is tested on a regular basis for arsenic. A random sample of 37 tests gave a sample mean of - = 7.3 ppb arsenic. It is known that o = this information indicate that the mean level of arsenic in this well is less than 8 ppb? Use the classical approach. Use a = 0.01 1.9 ppb for this type of data. Does What is the hypotheses for this problem? A: H, µ = 7.3 ppb vs HA µ 7.3 ppb С: Н. и %3D8.0 рpb us HA И < 8.0 ppb D : H, μ< 8.0 ppb us H μΣ8.0 ppb O A OB

In a random sample of size 11, N(mu, phi) population, obtain 90% confidence interval for standard deviation (phi) if the sample variance s^2 = 28.

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?