(F) p. 2 rognosticator makes 700 prediction correct with 546 of them. To a 1% le
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Question
(F) p. 2 rognosticator makes 700 prediction correct with 546 of them. To a 1% level of significance, can it be general, right more than 75% of the time? s regarding the outcomes of football games, and is asserted that he is, in A machine is designed to fill basketballs with an air pressure of 15 ppsi. 19 balls are examined, and it's found that they have a mean air pressure of 15.09 ppsi, with a standard deviation of .6 ppsi. To a 1% level of significance, can it be asserted that, in general, the standard deviation of the air pressure amounts is under 1 ppsi? Assume that the air pressure amounts are normally distributed.Explanation / Answer
Solution:-
5)
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: P < 0.75
Alternative hypothesis: P > 0.75
Note that these hypotheses constitute a one-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 = 0.01637
z = (p - P) / S.D
z = 1.833
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 1.833.
Thus, the P-value = 0.033.
Interpret results. Since the P-value (0.033) is greater than the significance level (0.01), we have to accept the null hypothesis.
From the above test we do not have sufficient evidence in the favor of the claim that he is in general right more than 75% of the time.
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