E. Calculate the estimate of the standard error of the mean where the sample sta
ID: 3178851 • Letter: E
Question
E. Calculate the estimate of the standard error of the mean where the sample standard deviation is 14.1522 and the sample size is 14. Enter your answer to four decimals (i.e. 1.1234).
F. Determine the calculated value of the test statistic (t) if the hypothesized value of mu is 23, the sample size is 11, the sample mean is 21.87, and the sample standard deviation is 8.27. Enter your response with the negative sign (if appropriate) rounded to two decimal places (i.e. -2.12).
G. Determine the critical value of the test statistic (t) where the sample size is 15, alpha is 0.03, and the alternative hypothesis is Ha: mu < 36.5. Enter your response to four decimal places (i.e. -2.1234) be sure to include the negative sign if the value is negative. Use Excel's TINV function and check to see that your answer is correct/reasonable, given the values in the t-table in your book.
H. Assume a state regulator wants to test whether the ethanol level in gasoline is significantly less than the required minimum. If the value of alpha being used is 0.05 and the p-value is 0.123, which of the following conclusions should be made?
1. Reject the null hypothesis and conclude the ethanol level is significantly less than the required minimum
2. Fail to reject the null hypothesis and conclude the ethanol level is significantly less than the required minimum
3. Reject the null hypothesis and conclude the ethanol level is not significantly less than the required minimum
4. Fail to reject the null hypothesis and conclude the ethanol level is not significantly less than the required minimum
5. none of these
I. Assume a company quality inspector has just completed testing ethanol levels in fuel samples from a random sample of stations owned by the company and that the calculated value of the test statistic t is 1.9. Also assume the critical value of t is +/- 2.093. Based on this information, which of the following conclusions would the quality control inspector make?
1. Reject the null hypothesis and conclude the ethanol level is too high
2. Fail to reject the null hypothesis and conclude the ethanol level is too high
3. Reject the null hypothesis and conclude the ethanol level is too low
4. Fail to reject the null hypothesis and conclude the ethanol level is too low
5. Reject the null hypothesis and conclude the ethanol level is within compliance
6. Fail to reject the null hypothesis and conclude the ethanol level is within compliance
7. none of these
J. A petroleum refiner selling automobile fuel in California, wanting to test whether their ethanol level is within the prescribed limits, has taken a systematic random sample, and has calculated the upper and lower limits of the confidence interval estimate of the percent ethanol as 21 to 24 percent. If the ethanol level, as required by the state of California must not be less than 23 percent, which of the following conclusions should be made?
1. Reject the null hypothesis and conclude the ethanol level is too high
2. Fail to reject the null hypothesis and conclude the ethanol level is too high
3. Reject the null hypothesis and conclude the ethanol level may be too low
4. Fail to reject the null hypothesis and conclude the ethanol level may be too low
5. Reject the null hypothesis and conclude the ethanol level is within compliance
6. Fail to reject the null hypothesis and conclude the ethanol level is within compliance
7. none of these
K. Calculate the value of the standard deviation of the sampling distribution of sample proportions (standard error of the proportion) where the hypothesized population proportion is 0.35 and the sample size is 1,802. Enter your response to three decimal places.
L. Determine the calculated value of the test statistic (z) if the hypothesized population proportion is 0.59, the sample size is 671, and the sample proportion is 0.78. Enter your response with the negative sign (if appropriate) to two decimal places (i.e. -2.12).
M. Determine the absolute (positive) value of the critical value of the test statistic (z) if alpha=0.08 for a two-tail test and enter it to two decimal places (i.e. 0.12). Use the NORMSINV function.
N. Determine the p-value if the alternative hypotheses is Ha:p < 0.25 and the calculated value of the test statistic (z) is 1.01. Use the NORMSDIST function and enter your response to four decimal places (i.e. 0.1234). Please contact me with questions.
O. Assume a quality control inspector has just completed testing the proportion conforming to standards from a random sample and that the calculated value of the test statistic z is -0.6. Based on this information, which of the following conclusions would the inspector make? Assume alpha = 0.05.
1. Reject the null hypothesis and conclude the proportion conforming to standards is too high
2. Fail to reject the null hypothesis and conclude the proportion conforming to standards is too high
3. Reject the null hypothesis and conclude the proportion conforming to standards is too low
4. Fail to reject the null hypothesis and conclude the proportion conforming to standards is too low
5. Reject the null hypothesis and conclude the proportion conforming to standards is acceptable
6. Fail to reject the null hypothesis and conclude the proportion conforming to standards is acceptable
7. none of these
P. Assume a quality control inspector has just completed testing the proportion conforming to standards from a random sample and that the p-value is 0.56. Based on this information, which of the following conclusions would the inspector make? Assume alpha = 0.05.
1. Reject the null hypothesis and conclude the proportion conforming to standards is too high
2. Fail to reject the null hypothesis and conclude the proportion conforming to standards is too high
3. Reject the null hypothesis and conclude the proportion conforming to standards is too low
4. Fail to reject the null hypothesis and conclude the proportion conforming to standards is too low
5. Reject the null hypothesis and conclude the proportion conforming to standards is acceptable
6. Fail to reject the null hypothesis and conclude the proportion conforming to standards is acceptable
7. none of these
Explanation / Answer
E)std error =std deviation/(n)1/2 =3.7823
F)std error std deviation/(n)1/2 =2.4935
test stat =(X-mean)/.std error =-0.453
G) critical value =-2.0462
H)4. Fail to reject the null hypothesis and conclude the ethanol level is not significantly less than the required minimum
I)6. Fail to reject the null hypothesis and conclude the ethanol level is within compliance
J)6. Fail to reject the null hypothesis and conclude the ethanol level is within compliance
K) std errror=(p(1-p)/n)1/2 =0.0112
L)std error =0.019
hence test stat=(phat-p)/std error =40.49
M)1.75
N)0.1562
O)6. Fail to reject the null hypothesis and conclude the proportion conforming to standards is acceptable
P)6. Fail to reject the null hypothesis and conclude the proportion conforming to standards is acceptable
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