based on a random sample of 640 college students, the mean amount of sleep college students. construct a 95% confidence interval for the mean amount of sleep per night for college studenrs.
Formula:
CI95 = mean + or - 1.96(sd/√n)
...where + or - 1.96 represents the 95% interval using a z-table, sd = standard deviation, and n = sample size.
Fill in the data and calculate the interval.
1) A sample of 49 observations is taken from a normal population. The sample mean is 55 and the sample standard deviation is 10. Determine the 99% confidence interval for the population mean.
2) The Fox TV network is considering replacing one of its primetime crime investigation shows with a new family-oriented comedy show. Before a final decision is made, network executives commission a sample of 400 viewers. After viewing the comedy, 250 indicated they would watch the new show and suggested it replace the crime investigation show.
A) Estimate the value of the population proportion.
B) Compute the standard error of the proportion.
C) Develop a 99% CI for the population proportion.
D) Interpret your findings
To construct a 95% confidence interval for the mean amount of sleep per night for college students based on a random sample, you would need the sample mean and the sample standard deviation.
Let's assume that the sample mean amount of sleep per night is x̄ and the sample standard deviation is s.
The formula to calculate the confidence interval is:
Confidence Interval = x̄ ± (Z * (s / √n))
Where:
- x̄ is the sample mean
- Z is the Z-score corresponding to the desired confidence level (in this case, 95% confidence level)
- s is the sample standard deviation
- n is the sample size
For a 95% confidence level, the Z-score is approximately 1.96 (you can use a standard normal distribution table or a calculator to find the exact value).
Given that you have a sample size of 640 college students, plug in the values into the formula:
Confidence Interval = x̄ ± (1.96 * (s / √n))
Since you haven't provided the actual values for x̄ and s, you cannot calculate the confidence interval directly. However, now you have the formula and the necessary values to calculate it once you have the sample mean and standard deviation.