Answer:
a) 95% confidence interval for the meancost, μ, of all recent weddings in this country = (22,550.95, 30,226.40)
.The 95% confidence interval is from $22,550.95 to $30,226.40.
b) For the interpretation of the result, option D is correct.
We can be 95% confident that the mean cost, μ, of all recent weddings in this country is somewhere within the confidence interval.
c) Option B is correct.
The population mean may or may not lie in this interval, but we can be 95% confident that it does.
Step-by-step explanation:
Sample size = 20
Sample Mean = $26,388.67
Sample Standard deviation = $8200
Confidence Interval for the population mean is basically an interval of range of values where the true population mean can be found with a certain level of confidence.
Mathematically,
Confidence Interval = (Sample mean) ± (Margin of error)
Sample Mean = 26,388.67
Margin of Error is the width of the confidence interval about the mean.
It is given mathematically as,
Margin of Error = (Critical value) × (standard Error of the mean)
Critical value will be obtained using the t-distribution. This is because there is no information provided for the population mean and standard deviation.
To find the critical value from the t-tables, we first find the degree of freedom and the significance level.
Degree of freedom = df = n - 1 = 20 - 1 = 19.
Significance level for 95% confidence interval
(100% - 95%)/2 = 2.5% = 0.025
t (0.025, 19) = 2.086 (from the t-tables)
Standard error of the mean = σₓ = (σ/√n)
σ = standard deviation of the sample = 8200
n = sample size = 20
σₓ = (8200/√20) = 1833.6
99% Confidence Interval = (Sample mean) ± [(Critical value) × (standard Error of the mean)]
CI = 26,388.67 ± (2.093 × 1833.6)
CI = 26,388.67 ± 3,837.7248
99% CI = (22,550.9452, 30,226.3948)
99% Confidence interval = (22,550.95, 30,226.40)
a) 95% confidence interval for the meancost, μ, of all recent weddings in this country = (22,550.95, 30,226.40)
.The 95% confidence interval is from $22,550.95 to $30,226.40.
b) The interpretation of the confidence interval obtained, just as explained above is that we can be 95% confident that the mean cost, μ,of all recent weddings in this country is somewhere within the confidence interval
c) A further explanation would be that the population mean may or may not lie in this interval, but we can be 95% confident that it does.
Hope this Helps!!!
