(a) Test H0 : p = 1/2 vs. Ha : p does not equal 1/2 for...

(a) Test H0 : p = 1/2 vs. Ha : p does not equal 1/2 for X ∼ Binomial(n=45,p), when we observe 16 successes.

(b) Calculate a 95% confidence interval for p for the data above.

(c) Calculate a 95% confidence interval for p when X ∼ Binomial(15,p) and we observe only successes

Expert Solution

orchestra answered 1 year ago

Suppose that you are testing the hypotheses H0: u=74 vs. HA: u does not equal 74....

Suppose that you are testing the hypotheses H0: u=74 vs. HA: u does not equal 74. A sample of size 51 results in a sample mean of 69 and a sample standard deviation of 1.8. a) What is the standard error of the mean? b) What is the critical value of t* for a 90% confidence interval? c) Construct a 90% confidence interval for mu. d) Based on the confidence interval, at a=0.100 can you reject H0?...

1. We want to test H0 : p ≥ 0.43 versus Ha : p < 0.43...

1. We want to test H0 : p ≥ 0.43 versus Ha : p < 0.43 . We know that n = 500 and p = 0.3990 . (a) What is the value of the test statistic? Round your test statistic to 2 digits after the decimal point. (To get an answer good to 2 digits, compute the standard error to 5 digits.) (b) What is the p-value of the test ? Round your p-value to 3 digits after the...

A test of H0: p = 0.4 versus Ha: p > 0.4 has the test statistic...

A test of H0: p = 0.4 versus Ha: p > 0.4 has the test statistic z = 2.52. Part A: What conclusion can you draw at the 5% significance level? At the 1% significance level? (6 points) Part B: If the alternative hypothesis is Ha: p ≠ 0.4, what conclusion can you draw at the 5% significance level? At the 1% significance level? (4 points) (10 points)

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...

For a test of population proportion H0: p = 0.6 versus Ha: p ≠0.6 , the...

For a test of population proportion H0: p = 0.6 versus Ha: p ≠0.6 , the test statistic equals 1.21. Find the P-value for this test.

Suppose that you are testing the hypotheses H0: p=0.18 vs. HA: p=/ 0.18. A sample of...

Suppose that you are testing the hypotheses H0: p=0.18 vs. HA: p=/ 0.18. A sample of size 150 results in a sample proportion of 0.25. a) Construct a 99% confidence interval for p. b) Based on the confidence interval, can you reject H0 at a =0.01? Explain. c) What is the difference between the standard error and standard deviation of the sample proportion? d) Which is used in computing the confidence interval?

5. For a test of H0 : p = p0 vs. H1 : p < p0,...

5. For a test of H0 : p = p0 vs. H1 : p < p0, the value of the test statistic z obs is -1.87. What is the p-value of the hypothesis test? (Express your answer as a decimal rounded to three decimal places.) 6. A pilot survey reveals that a certain population proportion p is likely close to 0.56. For a more thorough follow-up survey, it is desired for the margin of error to be no more than...

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

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.

You collect data and test the hypotheses H0: p = 0.50 Ha: p not equals...

You collect data and test the hypotheses H0: p = 0.50 Ha: p not equals 0.50, A P-value of 0.03 is obtained. Which of the following is true (hint: find α for each) ? A. A 99% confidence interval for p will not include the value 0.50. B. A 95% confidence interval for p will not include the value 0.50. C. A 90% confidence interval for p will not include the value 0.50. D. B and C. E. A...

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