The security department of a factory wants to know whether the true average time required by the night guard to walk his round is less than 10 minutes. In a random sample of 32 rounds, the night guard averaged 9.64 minutes while his rounds varied by a standard deviation of s = 1.1 minutes. Test, at significance level α = 0.05, whether there is evidence that the true average time it takes the night guard to walk his round is less than 10 minutes, by testing the hypotheses: H 0: μ = 10 mins H a: μ < 10 mins. Complete the test by filling in the blanks in the following: An estimate of the population mean is . The standard error is . The distribution is (examples: normal / t12 / chisquare4 / F5,6). The test statistic has value TS= . The P-value for this test is calculated to be (4 dec places) . Since the P-value is (smaller/larger) than. (2 dec places), there (is evidence/is no evidence) to reject the null hypothesis, H 0. There (is sufficient/is insufficient) evidence to suggest that the true average time it takes the night guard to walk his round, μ, is less than 10 minutes. Were any assumptions required in order for this inference to be valid? a: No - the Central Limit Theorem applies, which states the sampling distribution is normal for any population distribution. b: Yes - the population distribution must be normally distributed. Insert your choice (a or b): .
The security department of a factory wants to know whether the true average time required by the night guard to walk his round is less than 10 minutes. In a random sample of 32 rounds, the night guard averaged 9.64 minutes while his rounds varied by a standard deviation of s = 1.1 minutes.
Test, at significance level α = 0.05, whether there is evidence that the true average time it takes the night guard to walk his round is less than 10 minutes, by testing the hypotheses:
H 0: μ = 10 mins
H a: μ < 10 mins.
Complete the test by filling in the blanks in the following:
An estimate of the population mean is .
The standard error is .
The distribution is (examples: normal / t12 / chisquare4 / F5,6).
The test statistic has value TS= .
The P-value for this test is calculated to be (4 dec places) .
Since the P-value is (smaller/larger) than. (2 dec places),
there (is evidence/is no evidence) to reject the null hypothesis, H 0.
There (is sufficient/is insufficient) evidence to suggest that the true average time it takes the night guard to walk his round, μ, is less than 10 minutes.
Were any assumptions required in order for this inference to be valid?
a: No - the Central Limit Theorem applies, which states the sampling
b: Yes - the population distribution must be normally distributed.
Insert your choice (a or b): .
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