Question

In: Statistics and Probability

QUESTION 1: You are testing H0: µ = 0 against Ha: µ > 0 based on...

QUESTION 1:

You are testing H₀: µ = 0 against H_a: µ > 0 based on an SRS of 16 observations from a Normal population.

What values of the t statistic are statistically significant at the a = 0.005 level?

t < - 3.286 or t > 3.286

t > 2.947

t < - 3.252 or t > 3.252

QUESTION 2:

A study of commuting times reports the travel times to work of a random sample of 22 employed adults in Chicago. The mean is x¯¯¯x¯ = 33.33 minutes and the standard deviation is s = 25.89 minutes.

What is the standard error (±0.0001) of the mean?

Solutions

Expert Solution

Question 1:

For testing H₀: µ = 0 against H_a: µ > 0

This corresponds to right hand tail test.

we have, n = 16

df = 16 -1 = 15

And = 0.005

Using t-table, the critical value corresponding to df =15 for = 0.005 is t_c = 2.947

Since, t statistic is statistically significant at the a = 0.005 level

t > t_c i.e. t > 2.947

Answer : t > 2.947

Question 2:

We have

The standard error of the mean is given by

orchestra answered 2 years ago

Next > < Previous

Related Solutions

You are testing H0: µ = 0 against Ha: µ > 0 based on an SRS...

You are testing H0: µ = 0 against Ha: µ > 0 based on an SRS of 15 observations from a Normal population. What values of the t statistic are statistically significant at the a = 0.005 level? t < - 3.326 or t > 3.326 t > 2.977 t < - 3.286 or t > 3.286 To study the metabolism of insects, researchers fed cockroaches measured amounts of a sugar solution. After 2, 5, and 10 hours, they dissected...

Determine the p-value for testing: H0: µ = 15 Ha: µ > 15 when a random...

Determine the p-value for testing: H0: µ = 15 Ha: µ > 15 when a random sample of size 18 was taken from a normal population whose standard deviation is unknown and the value of the test statistic equals 2.35. The 98% confidence interval for the population proportion of successes when a random sample of size 80 was taken from a very large population and the number of successes in that sample was counted to be 20. No concluding statement is...

In testing H0: μ1 - μ2 = 0 versus Ha: μ1 - μ2 ≠ 0, the...

In testing H0: μ1 - μ2 = 0 versus Ha: μ1 - μ2 ≠ 0, the computed value of the test statistic is z = 1.98. The P-value for this two-tailed test is then: a. .0478 b. .2381 c. .4761 d. .0239 e. .2619

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

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...

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.

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...

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.

In a test of H0: μ = 200 against Ha: μ > 200, a sample of...

In a test of H0: μ = 200 against Ha: μ > 200, a sample of n = 120 observations possessed mean %5Cbar%7Bx%7D.svg x ¯ = 208 and standard deviation s = 38. Find the p-value for this test. Round your answer to 4 decimal places.

Suppose that you are testing the hypotheses H0: μ =11 vs. HA: μ <11 A sample...

Suppose that you are testing the hypotheses H0: μ =11 vs. HA: μ <11 A sample of size 64 results in a sample mean of 11.5 and a sample standard deviation of 2.4 a) What is the standard error of the mean? b) What is the critical value of t* for a 99 % confidenceinterval? c) Construct a 99%confidence interval for μ. d) Based on the confidence interval, at a =0.005 can you reject H0? Explain. 2)Before lending someone money,...

Subjects