A CEO of a firm claims that the mean work day of the firm\'s accountants is less
ID: 3154189 • Letter: A
Question
A CEO of a firm claims that the mean work day of the firm's accountants is less than 8.5 hours. A random sample of 35 of the firm's accountants has a mean work day of 8.2 hours with a standard deviation of 0.5 hour. At a = 0.01, test the CEO's claim? State the null and alternate hypotheses, and identify which represents the claim. Determine whether the hypothesis test is a left-tailed test, right tailed test, or two-tailed test Sketch a normal sampling distribution and shade the area for the P-value Calculate the P-value Compare the P-value with alpha Do you reject H_0 or do you fail to reject H_0 ? Interpret your decision From a random sample of 32 gas grills has a mean price of $630.90 and a standard deviation of $56.70. Construct a 91% confidence interval. Find a point estimate of the population mean price Verify that the conditions are met to construct an interval of confidence for the population mean price Calculate the standard of error Calculate the margin of error e. Interpret it Construct a 91 % confidence interval of the population mean price Interpret what does this interval of confidence mean. If we decrease the level of confidence, what would happen to margin of error? In a survey of 1006 adults from the US, 181 said that Abraham Lincoln was the greatest president. Find a point estimate for the population proportion of adults who say Abraham Lincoln was the greatest president. Verify that the conditions are met to construct an interval of confidence Calculate the standard of error Calculate the margin of error and interpret it Construct a 95 % confidence interval for the population proportion of adults who say Abraham Lincoln was the greatest president. Interpret what does this interval of confidence mean. lithe interval of confidence for the population of proportions of registered voters who will vote for your candidate is (0.39,0.47), then w hat would be sample proportion p be? If the interval of confidence for the population mean repair cost of a washing machine is (110,135), then what would be the margin of error ME?Explanation / Answer
3. In a survey of 1006...
a)
Note that
p^ = point estimate of the population proportion = x / n = 181/1006 = 0.179920477 [ANSWER]
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b)
As both the number of successes (181) and failures (1006-181) are greater than 15, then we can construct a confidence interval.
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c)
Also, we get the standard error of p, sp:
sp = sqrt[p^ (1 - p^) / n] = 0.012110701 [ANSWER, STANDARD ERROR]
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d)
Now, for the critical z,
alpha/2 = 0.025
Thus, z(alpha/2) = 1.959963985
Thus,
Margin of error = z(alpha/2)*sp = 0.023736538 [ANSWER]
Hence, we we are 95% confident our confidence interval, when centered around 0.1799, and has margin of error 0.02374, captures the true population proportion.
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e)
lower bound = p^ - z(alpha/2) * sp = 0.156183939
upper bound = p^ + z(alpha/2) * sp = 0.203657015
Thus, the confidence interval is
( 0.156183939 , 0.203657015 ) [ANSWER]
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f)
We are 95% confident that the true population proportion of those who say that Abraham Lincoln was the greatest president is between 0.156183939 and 0.203657015. [ANSWER]
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