Please solve these questions and why we choose the answers. Thanks! 15. The nico
ID: 3354475 • Letter: P
Question
Please solve these questions and why we choose the answers. Thanks!
15. The nicotine content in cigarettes of a certain brand is Normally distributed with a standard deviation of = 0.1 milligrams. The brand advertises that the mean nicotine content of their cigarettes is = 1.5 milligrams, but measurements on a random sample of 100 cigarettes of this brand gave a mean of x = 1.53. Is this evidence that the mean nicotine content is actually higher than advertised? To answer this, test the hypotheses H: 1.5 versus Ha: > 1.5. Determine whether each of the following statements is true or false. A) The probability that Ho is true is 0.05. B) The data were statistically significant at = 0.05. C) At the 5% significance level, H, should be rejected. D) Even if nicotine content in cigarettes of this brand were not quite Normally distributed, the test would still be valid. 16. A college student is doing some research on the cost of one-bedroom apartments in town. He has randomly selected 25 apartments for which the price was published. The average price for these apartments is x = $652. He will assume that price follows roughly a Normal distribution. Based on prices from previous years, a real estate agent gives him the information that is approximately $55. A 95% confidence interval for is found to be 652 ± 21.56 = ($630.44, $673.56). Determine which of the following statements is TRUE A) A test of the hypotheses Ho: -650 versus Ha: 650 would be rejected at the B) C) D) 0.05 level. A test of the hypotheses H0: -650 versus Ha: > 650 would be rejected at the 0.05 level A test of the hypotheses His -675 versus Ha: 0.05 level All of the above 675 would be rejected at the
Explanation / Answer
Solution:-
15)
A) False
B) True
C) True
D) True
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: < 15
Alternative hypothesis: > 15
Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected if the sample mean is too small.
Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method is a one-sample z-test.
Analyze sample data. Using sample data, we compute the standard error (SE), z statistic test statistic (z).
SE = s / sqrt(n)
S.E = 0.01
z = (x - ) / SE
z = 3
where s is the standard deviation of the sample, x is the sample mean, is the hypothesized population mean, and n is the sample size.
The observed sample mean produced a z statistic test statistic of 3.
Thus the P-value in this analysis is 0.0013.
Interpret results. Since the P-value (0.0013) is less than the significance level (0.05), we have to reject the null hypothesis.
16)
C) A test of the hypothesis H0: = 675 versus Ha is not equal to 675 would be rejected at the 0.05 level.
SInce 95% confidence interval contains all values less than 675 hence we have to reject the null hypothesis.