sample of 80 people randomly asked in casino shows that average lost per person is $160 with a sample standard deviation s=$40. Based on this data create a 95% confidence interval for population mean.
Your school subject is probably Statistics.
95% confidence = mean ± 1.96 SEmean
SEm = SD/√(n-1)
To calculate the confidence interval for the population mean, we can use the formula:
CI = X̄ ± Z * (s / √n)
Where:
- X̄ is the sample mean
- Z is the Z-value for the desired confidence level
- s is the sample standard deviation
- n is the sample size
In this case, the sample mean (X̄) is $160, the sample standard deviation (s) is $40, and the sample size (n) is 80.
To find the Z-value for a 95% confidence level, we can use a Z-table or a statistical calculator. The Z-value for a 95% confidence level is approximately 1.96.
Now, we can substitute the values into the formula:
CI = 160 ± 1.96 * (40 / √80)
Calculating the expression within the parentheses:
40 / √80 ≈ 4.48
Then, substituting this value into the formula:
CI = 160 ± 1.96 * 4.48
Calculating the expression within the square root:
1.96 * 4.48 ≈ 8.79
Finally, substituting this value into the formula:
CI = 160 ± 8.79
This gives us the range of the confidence interval. To find the upper and lower bounds, we can add and subtract the value calculated above from the sample mean:
Upper bound = X̄ + Z * (s / √n)
Upper bound = 160 + 8.79 ≈ 168.79
Lower bound = X̄ - Z * (s / √n)
Lower bound = 160 - 8.79 ≈ 151.21
Therefore, the 95% confidence interval for the population mean is approximately $151.21 to $168.79.