Statistical Analysis Quiz

A researcher wants to estimate the mean weight of packages shipped by a company. The population standard deviation is known to be 5 kg. The researcher wants to be 95% confident that the margin of error is 1 kg (z α/2 =1.96). How large should the sample size be?

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A researcher wants to understand employee job satisfaction in a large company. They divide the employees into departments (HR, Sales, Marketing, etc.) and then randomly select a few employees from each department to survey. What type of sampling is this?

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A survey of 25 employees reveals an average satisfaction score of 7.8 out of 10. The overall population mean satisfaction score is 8.2. Calculate the sampling error.

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A researcher wants to estimate the average height of adult males in a city. From a sample of 50 men, the sample mean is found to be 175 cm. Assuming the population standard deviation is known to be 10 cm, calculate the 95% confidence interval for the population mean (Z=1.96).

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A random sample of 25 students has a mean test score of 78 with a sample standard deviation of 10. Calculate the 95% confidence interval for the population mean test score (t=2.064).

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A sample of 200 households shows that 120 have access to high-speed internet. Find the 90% confidence interval for the population proportion of households with high-speed internet access (z=1.645).

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An ecologist is studying the average lifespan of a certain type of bird. The population standard deviation is unknown, so they conduct a preliminary study and find a sample standard deviation of 3 years. The ecologist wants to be 95% (t = 1.96) confident that the margin of error is within 0.5 years of the population mean. How large should the sample size be?

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A quality control analyst at a manufacturing plant wants to verify the average diameter of metal rods produced. The factory produces 2,000 rods each month. A random sample of 40 rods is selected, and the average diameter is measured at 5 cm. The population standard deviation is known to be 0.2 cm. Construct a 90% (z = 1.645) confidence interval for the true mean diameter of all rods, applying the finite population correction.

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A researcher wants to survey a town's population of 10,000 residents to understand their views on a new community project. They aim to achieve a margin of error of 5% for the survey. Using Slovin's formula, calculate the sample size needed if the desired confidence level is 95%.

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In a recent survey, 60% of a random sample of 200 residents of a city favored constructing a new public park. Construct a 95% confidence interval for the true proportion of the city's residents who favor the park.

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