Confidence Intervals for a Population Mean (University)
Free printable university statistics worksheet constructing z- and t-confidence intervals for a mean, with z* computed by inverting the standard normal CDF and t* from the standard Student's t table (df = n - 1).
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Probability & Statistics · Math worksheet
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Math
Confidence Intervals for a Population Mean
Use xbar +/- z* sigma/sqrt(n) when sigma is known, and xbar +/- t* s/sqrt(n) with df = n - 1 when sigma is unknown. Round interval endpoints to 2 decimal places and margins of error to 3.
- 1.A random sample of n = 49 measurements of download speed at a campus (Mbps) has sample mean 85 and population standard deviation sigma 9.2. Find the margin of error for a 95% confidence interval for the population mean (use the z-distribution). Round to 3 decimal places.
- 2.A random sample of n = 16 measurements of sleep duration of first-year students (hours) has sample mean 7.6 and sample standard deviation s 1.2. Construct a 95% confidence interval for the population mean using the t-distribution (df = 15). Round the endpoints to 2 decimal places.
- 3.A random sample of n = 64 measurements of sleep duration of first-year students (hours) has sample mean 7 and population standard deviation sigma 1.8. Construct a 95% confidence interval for the population mean using the z-distribution. Round the endpoints to 2 decimal places.
- 4.A random sample of n = 64 measurements of sleep duration of first-year students (hours) has sample mean 6 and population standard deviation sigma 2. Find the margin of error for a 99% confidence interval for the population mean (use the z-distribution). Round to 3 decimal places.
- 5.A random sample of n = 20 measurements of download speed at a campus (Mbps) has sample mean 75 and sample standard deviation s 8.5. Construct a 95% confidence interval for the population mean using the t-distribution (df = 19). Round the endpoints to 2 decimal places.
- 6.A random sample of n = 36 measurements of download speed at a campus (Mbps) has sample mean 90 and population standard deviation sigma 7.1. Find the margin of error for a 99% confidence interval for the population mean (use the z-distribution). Round to 3 decimal places.
- 7.A random sample of n = 16 measurements of sleep duration of first-year students (hours) has sample mean 6 and sample standard deviation s 1.7. Construct a 95% confidence interval for the population mean using the t-distribution (df = 15). Round the endpoints to 2 decimal places.
- 8.A random sample of n = 49 measurements of download speed at a campus (Mbps) has sample mean 70 and population standard deviation sigma 5. Construct a 95% confidence interval for the population mean using the z-distribution. Round the endpoints to 2 decimal places.
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