Question

A Patent Medicine Company supervisor assumes that the bottling machine is operating properly if only 5 percent of the processed bottles are not full. A random sample of 100 bottles had 7 bottles that weren’t full. Using a significance level of .01, conduct a test to see if the machine is operating properly. 10. According to Management Accounting, salary figures for certified management accountants (CMAs) who are in the field less than 1 year are normally distributed with a mean of $31,129. A random sample of 15 firstyear CMAs in Denver produces a mean salary of $32,279, with a standard deviation of $1,797. Test the hypothesis that the mean for all Denver firstyear CMAs is not equal to $31,129. Use the .05 level of significance.

1. State the null hypothesis H0: _____________

2. State the alternative hypothesis H1: _____________

3. What is the test statistic used for the test (z or t)

4. State the significance or alpha (?) level

5. Determine the p-value.

6. Do you or do you not reject the null hypothesis? Why?

7. Write a clear conclusion using a complete sentence.

Answer 1

Solution:-

9)

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: P = 0.05
Alternative hypothesis: P 0.05

Note that these hypotheses constitute a two-tailed test.  

Formulate an analysis plan. For this analysis, the significance level is 0.01. The test method, shown in the next section, is a one-sample z-test.

Analyze sample data. Using sample data, we calculate the standard deviation (S.D) and compute the z-score test statistic (z).

S.D = sqrt[ P * ( 1 - P ) / n ]

S.D = 0.02179
z = (p - P) /S.D

z = 0.92

where P is the hypothesized value of population proportion in the null hypothesis, p is the sample proportion, and n is the sample size.

Since we have a two-tailed test, the P-value is the probability that the z-score is less than - 0.92 or greater than 0.92.

Thus, the P-value = 0.358

Interpret results. Since the P-value (0.358) is greater than the significance level (0.01), we cannot reject the null hypothesis.

Do not reject H₀.

From the above test we have sufficient evidence in the favor of the claim that the machine is operating properly.