A sample of size n = 52 has sample mean x = 53.4 and sample standard deviation s = 9.4. Part 1 of 2 Construct a 90% confidence interval for the population mean ?. Round the answers to one decimal place. A 90% confidence interval for the population mean ? is 51.2 < ? < 55.6. Part 2 of 2 If the sample size were n = 38, would the confidence interval be narrower or wider? The confidence interval would be (Choose one)
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A sample of size n = 42 has sample mean x = 53.1 and sample standard deviation s = 8.2. Construct an 80% confidence interval for the population mean μ. Round the answers to one decimal place. An 80% confidence interval for the population mean μ is 51.5 < μ < 54.7. If the sample size were n = 31, would the confidence interval be narrower or wider? The confidence interval would be (Choose one)
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A simple random sample of size $n$ is drawn. The sample mean, $\bar{x},$ is found to be $18.4,$ and the sample standard deviation, $s$, is found to be $4.5 .$ (a) Construct a $95 \%$ confidence interval about $\mu$ if the sample size, $n,$ is 35 (b) Construct a $95 \%$ confidence interval about $\mu$ if the sample size, $n,$ is $50 .$ How does increasing the sample size affect the margin of error, $E ?$ (c) Construct a $99 \%$ confidence interval about $\mu$ if the sample size, $n,$ is $35 .$ Compare the results to those obtained in part (a). How does increasing the level of confidence affect the margin of error, $E ?$ (d) If the sample size is $n=15,$ what conditions must be satisfied to compute the confidence interval?
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