Question

In: Statistics and Probability

Consider the following hypothesis test: H 0:   50 H a:  > 50 A sample of 60 is used...

Consider the following hypothesis test:

H 0:   50

H a:  > 50

A sample of 60 is used and the population standard deviation is 7. Use the critical value approach to state your conclusion for each of the following sample results. Use  = .05.

a. With  = 52.5, what is the value of the test statistic (to 2 decimals)?
  

Can it be concluded that the population mean is greater than 50?
SelectYesNoItem 2

b. With  = 51, what is the value of the test statistic (to 2 decimals)?
  

Can it be concluded that the population mean is greater than 50?
SelectYesNoItem 4

c. With  = 51.8, what is the value of the test statistic (to 2 decimals)?
  

Can it be concluded that the population mean is greater than 50?
SelectYesNoItem 6

Solutions

Expert Solution

= 50

n = 60

= 7

The z-critical value for a right-tailed test, for a significance level of α=0.05 is. zc = 1.64

(a) = 52.5

z = 2.77

As z stat falls in the rejection area, we reject the Null hypothesis.

Can it be concluded that the population mean is > 50 : Yes

(b) = 51

z = 1.11

As z stat does not fall in the rejection area, we fail to reject the Null hypothesis.

Can it be concluded that the population mean is > 50 : No

(c)   = 51.8

z = 1.99

As z stat falls in the rejection area, we reject the Null hypothesis.

Can it be concluded that the population mean is > 50 : Yes


Related Solutions

Consider the following hypothesis test: H 0:   50 H a:  > 50 A sample of 50 is used...
Consider the following hypothesis test: H 0:   50 H a:  > 50 A sample of 50 is used and the population standard deviation is 7. Use the critical value approach to state your conclusion for each of the following sample results. Use  = .05. a. With x (with line over top of x) = 52.5, what is the value of the test statistic (to 2 decimals)? b. With x = 51, what is the value of the test statistic (to 2 decimals)? c....
Consider the following hypothesis test: H 0:   50 H a:  > 50 A sample of 70 is used...
Consider the following hypothesis test: H 0:   50 H a:  > 50 A sample of 70 is used and the population standard deviation is 7. Use the critical value approach to state your conclusion for each of the following sample results. Use  = .05. a. With x = 52.5, what is the value of the test statistic (to 2 decimals)? b.  With x = 51, what is the value of the test statistic (to 2 decimals)? c. With x = 51.8, what is the...
Consider the following hypothesis test: H 0:   50 H a:  > 50 A sample of 55 is used...
Consider the following hypothesis test: H 0:   50 H a:  > 50 A sample of 55 is used and the population standard deviation is 7. Use the critical value approach to state your conclusion for each of the following sample results. Use  = .05. a. With  = 52.5, what is the value of the test statistic (to 2 decimals)? Can it be concluded that the population mean is greater than 50? SelectYesNoItem 2 b. With  = 51, what is the value of the test statistic...
Consider the following hypothesis test: H 0:   50 H a:  > 50 A sample of 65 is used...
Consider the following hypothesis test: H 0:   50 H a:  > 50 A sample of 65 is used and the population standard deviation is 7. Use the critical value approach to state your conclusion for each of the following sample results. Use  = .05. a. With  = 52.5, what is the value of the test statistic (to 2 decimals)? Can it be concluded that the population mean is greater than 50? SelectYesNoItem 2 b. With  = 51, what is the value of the test statistic...
Consider the following hypothesis test: H 0:   50 H a:  > 50 A sample of 55 is used...
Consider the following hypothesis test: H 0:   50 H a:  > 50 A sample of 55 is used and the population standard deviation is 8. Use the critical value approach to state your conclusion for each of the following sample results. Use  = .05. With  = 52.5, what is the value of the test statistic (to 2 decimals)?    Can it be concluded that the population mean is greater than 50? SelectYesNoItem 2 b. With  = 51, what is the value of the test statistic...
Consider the following hypothesis test: H 0:   20 H a:  < 20 A sample of 50 provided a...
Consider the following hypothesis test: H 0:   20 H a:  < 20 A sample of 50 provided a sample mean of 19.4. The population standard deviation is 2. a. Compute the value of the test statistic (to 2 decimals). b. What is the p-value (to 3 decimals)? c. Using  = .05, can it be concluded that the population mean is less than 20? d. Using  = .05, what is the critical value for the test statistic? e. State the rejection rule: Reject H 0...
Consider the following hypothesis test: H 0:  = 17 H a:   17 A sample of 40 provided a...
Consider the following hypothesis test: H 0:  = 17 H a:   17 A sample of 40 provided a sample mean of 14.31. The population standard deviation is 5. a. Compute the value of the test statistic (to 2 decimals). (If answer is negative, use minus “-“ sign.) b. What is the p-value (to 4 decimals)? c. Using  = .05, can it be concluded that the population mean is not equal to 17? SelectYesNoItem 3 Answer the next three questions using the critical value...
Consider the following hypothesis test: H(0): mu ≥ 10 H(a): mu < 10 The sample size...
Consider the following hypothesis test: H(0): mu ≥ 10 H(a): mu < 10 The sample size is 120 and the population standard deviation is assumed known with σ = 5. Use alpha = .05. If the population mean is 9, what is the probability of making a Type II error if the actual population mean is 8 (to 4 decimals)? Please provide the appropriate formula in excel for solving this problem.
Consider the following hypothesis test: H 0: u = 16 H a: u ≠ 16 A...
Consider the following hypothesis test: H 0: u = 16 H a: u ≠ 16 A sample of 50 provided a sample mean of 14.13. The population standard deviation is 3. a. Compute the value of the test statistic (to 2 decimals). (If answer is negative, use minus “-“ sign.) 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? (yes, no) Answer the next three...
Consider the following hypothesis test. H0: μ ≤ 50 Ha: μ > 50 A sample of...
Consider the following hypothesis test. H0: μ ≤ 50 Ha: μ > 50 A sample of 60 is used and the population standard deviation is 8. Use the critical value approach to state your conclusion for each of the following sample results. Use α = 0.05. (Round your answers to two decimal places.) (a) x = 52.3 Find the value of the test statistic. = State the critical values for the rejection rule. (If the test is one-tailed, enter NONE...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT