8. Sports car owners i th n a town complain that the state vehicle inspection st
ID: 3064531 • Letter: 8
Question
8. Sports car owners i th n a town complain that the state vehicle inspection station judges frorn family-style cars. Previous records indicate that 30% of all eir cars differently Passenger cars fail the inspection on the first time through. In a random sample of inspection on the first time through. Is there sufficient evidence to i ndicate that the percentage of first failures for sports cars is higher than th e percentage for all passenger cars? 9. Food-borne illness was attributed to Salmonella enteritidis. Epidemiologists determined that the source of the illness was ice cream. WHAT. I'm shook. They sampled nine production runs from the company that had produced the ice cream to determine the level of S. enteritidis in the ice cream. These levels (MPN/g) are as follows: .593 142 329 .691 231 .793 519 392 418 Use these data to determine whether the average level of S. enteritidis in the ice cream is greater than 0.3 MPN/g, a level that is considered to be very dangerous.Explanation / Answer
Solution:-
8)
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: P < 0.30
Alternative hypothesis: P > 0.30
Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected only if the sample proportion is too small.
Formulate an analysis plan. For this analysis, the significance level is 0.05. 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 () and compute the z-score test statistic (z).
= sqrt[ P * ( 1 - P ) / n ]
= 0.03742
z = (p - P) /
z = 2.67
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 one-tailed test, the P-value is the probability that the z-score is greater than 2.67.
Thus, the P-value = 0.0038.
Interpret results. Since the P-value (0.0038) is less than the significance level (0.05), we cannot accept the null hypothesis.
From the above test we have sufficient evidence in the favor of the claim that the percentage of first failures of the sports car is higher than the percentage for all passenger cars.
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