Confidence Intervals; Am I correct on these 2 problems?

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In summary, the conversation discusses the calculation of the margin of error and a confidence interval for the mean trading volume of a particular stock based on a random sample of 35 trading days. The margin of error is calculated to be 4.19, and the confidence interval using a Z interval is (38.64, 40.32). Both calculations are based on a 95% confidence level and assume a population standard deviation of 15.07.
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A random sample of 35 trading days is taken and the volume of a particular stock is recorded to determine whether the mean volume of the stock has changed from its 2007 value of 35.14 million shares. The sample resulted in a mean trading volume of = 39.48. Assuming a population standard deviation of 15.07, compute the margin of error for a 95% confidence interval for m. I got 4.19 Is this correct?

Also, A random sample of 35 trading days is taken and the volume of a particular stock is recorded to determine whether the mean volume of the stock has changed from its 2007 value of 35.14 million shares. The sample resulted in a mean trading volume of = 39.48. Assuming a population standard deviation of 15.07, calculate a 95% confidence interval for m using a Z interval. I got (38.64, 40.32)
Is that correct or can it not be computed?
 
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Yes, your answer for the margin of error is correct. For the confidence interval, you are also correct.
 

Related to Confidence Intervals; Am I correct on these 2 problems?

1. What is a confidence interval?

A confidence interval is a range of values that is likely to contain the true value of a population parameter with a certain level of confidence. It is often used in statistical inference to estimate the range of values for a population parameter based on a sample of data.

2. How do you calculate a confidence interval?

The formula for calculating a confidence interval depends on the type of data and the population distribution. In general, a confidence interval is calculated by taking the point estimate (such as the sample mean) and adding or subtracting the margin of error, which is determined by the sample size and the desired level of confidence.

3. What does a confidence level of 95% mean?

A confidence level of 95% means that if the same population is sampled repeatedly, 95% of the time the calculated confidence interval will contain the true population parameter. In other words, there is a 95% probability that the true population parameter falls within the calculated confidence interval.

4. How do confidence intervals help in data analysis?

Confidence intervals help in data analysis by providing a range of values for a population parameter that is likely to contain the true value. This can help to make more accurate inferences about a population based on a sample of data. Additionally, confidence intervals can help to identify statistically significant differences between groups or variables.

5. Can you have a confidence interval with a sample size of 1?

No, a confidence interval requires a sample size of at least 2 in order to calculate a standard deviation and determine the margin of error. A single data point does not provide enough information to estimate the range of values for a population parameter with a certain level of confidence.

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