-in the 200censasthe 50called"longfromrecivedbyoneofeverysix hausholdcontained52 questionragingfromyouoccuption and income all the wayse whether you had both tub.According to the U,S census bureaw the mean completion time for the long from is 38 minutes .Assuming astandard deviation of 5minutey and a simple random sample of 50 person who filled out the long form.
To analyze the given information, it seems that in the 2000 census, there was a long form sent to households. This form contained 52 questions, including inquiries about occupation, income, and whether the household had a bathtub. According to the U.S. Census Bureau, the average time taken to complete the long form was 38 minutes, with a standard deviation of 5 minutes.
In this case, we have a random sample of 50 people who filled out the long form. We can use this information to make inferences about the population parameters.
If we assume that the completion times of the long form are normally distributed, and we have a simple random sample, we can use the properties of the normal distribution to perform statistical analyses.
For example, we could calculate confidence intervals to estimate the true mean completion time for the population based on the sample mean and standard deviation. We could also conduct hypothesis tests to determine if the mean completion time is significantly different from a certain value.
It's important to note that without more specific data or a clear research question, a more detailed analysis cannot be provided.
To answer your question step-by-step:
Step 1: Determine the given information:
- The long form in the 2000 Census contains 52 questions.
- The mean completion time for the long form is 38 minutes.
- The standard deviation is 5 minutes.
- A simple random sample of 50 people who filled out the long form is taken.
Step 2: Identify the formula for the sample mean:
- The formula for the sample mean is: x̄ = μ
Step 3: Calculate the sample mean:
- Plug in the given information into the formula: x̄ = 38 minutes
Step 4: Determine the standard error of the sample mean:
- The formula for the standard error of the sample mean is: SE = σ/√n
- Where σ is the standard deviation and n is the sample size.
Step 5: Calculate the standard error:
- Plug in the given information into the formula: SE = 5 minutes / √50
Step 6: Calculate the margin of error:
- The margin of error is the value added to and subtracted from the sample mean to create the confidence interval.
- The majority of confidence intervals use a 95% confidence level, which corresponds to a Z-value of 1.96.
- The margin of error formula is: ME = Z * SE
Step 7: Calculate the margin of error:
- Plug in the calculated standard error and a Z-value of 1.96 into the formula: ME = 1.96 * (5 minutes / √50)
Step 8: Calculate the lower and upper bounds of the confidence interval:
- The lower bound of the confidence interval is the sample mean minus the margin of error: LB = x̄ - ME
- The upper bound of the confidence interval is the sample mean plus the margin of error: UB = x̄ + ME
Step 9: Calculate the lower and upper bounds of the confidence interval:
- Plug in the calculated sample mean and margin of error into the respective formulas:
- LB = 38 minutes - (1.96 * (5 minutes / √50))
- UB = 38 minutes + (1.96 * (5 minutes / √50))
Step 10: Calculate the lower and upper bounds of the confidence interval:
- Calculate the values for LB and UB using a calculator or spreadsheet.
By following these steps, you can calculate the lower and upper bounds of the confidence interval for the completion time of the long form in the given scenario.