To test the hypothesis H0 : µ = 5 vs. Ha : µ 6= 5, a...

To test the hypothesis H0 : µ = 5 vs. Ha : µ 6= 5, a random sample of 18 elements is selected which yielded a sample mean of x¯ = 4.6 and a sample standard deviation of s = 1.2. The value of the test statistic is about:

(a) −2.121 (b) −1.923 (c) −1.414 (d) 0.345 (e) 1.455

Solutions

Expert Solution

n = 18

sample mean = 4.6

sample sd = 1.2

Assuming that the data is normally distributed, also as the population sd is not given, we will calculate t stat

t = -0.4. / 0.2828

t = -1.414

ANS : (c) −1.414

orchestra answered 1 year ago

Next > < Previous

Related Solutions

5. Consider the hypothesis test H0 : µ = 18, Ha :µ ≠ 18. A sample...

5. Consider the hypothesis test H0 : µ = 18, Ha :µ ≠ 18. A sample of size 20 provided a sample mean of 17 and a sample standard deviation of 4.5. a. 3pts.Compute the test statistic. b.3pts. Find the p-value at the 5% level of significance, and give the conclusion. c. 5pts.Make a 99% confidence interval for the population mean. d. 5pts.Suppose you have 35 observations with mean17 and S.d. 4.5. Make a 90% confidence interval for the population...

Consider the test of H0 : µ = 300 Vs. Ha : µ ≠ 300 using...

Consider the test of H0 : µ = 300 Vs. Ha : µ ≠ 300 using a random sample of 36 values and α = 5%. Assume that σ = 40. Find the power of the test when µa = 285.

2. Suppose we have the hypothesis test H0 : µ = 200 Ha : µ >...

2. Suppose we have the hypothesis test H0 : µ = 200 Ha : µ > 200 in which the random variable X is N(µ, 10000). Let the critical region C = {x : x ≥ c}. Find the values of n and c so that the significance level of this test is α = 0.03 and the power of µ = 220 is 0.96.

We want to test H0 : µ ≥ 200 versus Ha : µ < 200 ....

We want to test H0 : µ ≥ 200 versus Ha : µ < 200 . We know that n = 324, x = 199.700 and, σ = 6. We want to test H0 at the .05 level of significance. For this problem, round your answers to 3 digits after the decimal point. 1. What is the value of the test statistic? 2. What is the critical value for this test? 3. Using the critical value, do we reject or...

Suppose an experimenter wishes to test H0: µ = 100 vs H1: µ ≠ 100 at...

Suppose an experimenter wishes to test H0: µ = 100 vs H1: µ ≠ 100 at the α = 0.05 level of significance and wants 1 – β to equal 0.60 when µ = 103. What is the smallest (i.e. cheapest) sample size that will achieve the objective? Assume the variable being measured is normally distributed with σ = 14.

A t statistic was used to conduct a test of the null hypothesis H0: µ =...

A t statistic was used to conduct a test of the null hypothesis H0: µ = 11 against the alternative Ha: µ ≠ 11, with a p-value equal to 0.042. A two-sided confidence interval for µ is to be considered. Of the following, which is the largest level of confidence for which the confidence interval will NOT contain 11? A 90% confidence level A 92% confidence level A 96% confidence level A 97% confidence level A 98% confidence level

Consider the following hypothesis test: H0: ? = 16 Ha: ? ? 16 A sample of...

Consider the following hypothesis test: H0: ? = 16 Ha: ? ? 16 A sample of 40 provided a sample mean of 14.17. The population standard deviation is 6. a. Compute the value of the test statistic (to 2 decimals). b. What is the p-value (to 4 decimals)? c. Using ? = .05, can it be concluded that the population mean is not equal to 16? Answer the next three questions using the critical value approach. d. Using ? =...

Consider a general one-sided hypothesis test on a population mean µ with null hypothesis H0 :...

Consider a general one-sided hypothesis test on a population mean µ with null hypothesis H0 : µ = 0, alternative hypothesis Ha : µ > 0, and Type I Error α = 0.02. Assume that using a sample of size n = 100 units, we observe some positive sample mean x > 0 with standard deviation s = 5. (a) Calculate the Type II Error and the power of the test assuming the following observed sample means: (i) x =...

Consider the following hypothesis test. H0: μ ≥ 70 Ha: μ < 70

You may need to use the appropriate technology to answer this question. Consider the following hypothesis test. H0: μ ≥ 70 Ha: μ < 70 A sample of 100 is used and the population standard deviation is 12. Compute the p-value and state your conclusion for each of the following sample results. Use α = 0.01. (a) x = 68.5 Find the value of the test statistic. Find the p-value. (Round your answer to four decimal places.) p-value = State...

For a hypothesis test of H0: p = 0.65 against the alternative Ha: p < 0.65,...

For a hypothesis test of H0: p = 0.65 against the alternative Ha: p < 0.65, the z test statistic is found to be -2.35. What can be said about his finding? The finding is significant at both α = 0.05 and α = 0.01. The finding is significant at α = 0.05 but not at α = 0.01. The finding is significant at α = 0.01 but not at α = 0.05. The finding is not significant at α...

Subjects