< Question 10 of 13 > A company produces precision 1000-millimeter rulers. The actual distribution of the lengths of the rulers produced by this company is Normal, with mean $\mu$ and standard deviation $\sigma = 0.02$ millimeters. Suppose I select a simple random sample of four of the rulers produced by the company and I measure their lengths in millimeters. The sample yields $\bar{x} = 1000$. A 90% confidence interval for $\mu$ based on these data is $1000 \pm 0.0115$ $1000 \pm 0.0196$ $1000 \pm 0.0165$ $1000 \pm 0.0082$ Incorrect Answer Attempt 1
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The population mean is $\mu$. The population standard deviation is $\sigma = 0.02$ millimeters. The sample size is $n = 4$. The sample mean is $\bar{x} = 1000$ millimeters. We need to construct a 90% confidence interval for the population mean $\mu$. Show more…
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A company produces precision 1000-millimeter rulers. The actual distribution of the lengths of the rulers produced by this company is normal, with mean μ and standard deviation σ = 0.02 millimeters. Suppose we select a simple random sample of four of the rulers produced by the company and measure their lengths in millimeters. The sample yields a z-value of 1.96. A 90% confidence interval for μ is: 1000 ± 0.0082 1000 ± 0.0115 1000 ± 0.0165 1000 ± 0.0196
Ajiboye T.
A company produces precision 1-meter (1000 mm) rulers. The actual distribution of lengths of the rulers produced by this company is normal with mean μ and standard deviation 0.02 mm. Suppose we select a simple random sample of four of the rulers produced by the company and measure their lengths in millimeters. The results of these four measurements are as follows: 1000.01 999.98 1000.00 1000.01 We will use a 90% confidence interval to estimate the mean length of 1m rulers. We will use a Z-procedure to calculate the margin of error and the confidence interval to five decimal places. Table C shows that we are 90% confident that the mean length of 1m rulers is between mm and mm.
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A random sample of 100 observations from a normally distributed population possesses a mean equal to 76.7 and a standard deviation equal to $7.9 .$ a. Find a $90 \%$ confidence interval for $\mu$. b. What do you mean when you say that a confidence coefficient is $.90 ?$ c. Find a $95 \%$ confidence interval for $\mu$. d. What happens to the width of a confidence interval as the value of the confidence coefficient is increased while the sample size is held fixed? e. Would your confidence intervals of parts a and $\mathbf{c}$ be valid if the distribution of the original population were not normal? Explain.
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