11. Miss Romero noted that the mean scores of a random sample of 15 Grade 8 students who had taken a special test was 80.5. If the standard deviation of the scores was 3.1 and the sample came from approximately normal population, find the point and interval estimates of the population mean using 95% confidence
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Answer:
To find the point estimate of the population mean, we simply use the mean of the sample, which is 80.5.
To find the interval estimate using a 95% confidence level, we need to use a t-distribution since the population standard deviation is unknown and the sample size is relatively small (n=15).
The formula for the confidence interval is:
x̄ ± t(α/2, n-1) * (s/√n)
Where:
x̄ = sample mean (80.5)
t(α/2, n-1) = t-value with (n-1) degrees of freedom and a level of significance of α/2 (α=0.05, so α/2 = 0.025). From the t-distribution table, the t-value is 2.144.
s = sample standard deviation (3.1)
n = sample size (15)
Substituting the values into the formula, we get:
80.5 ± 2.144 * (3.1/√15)
Solving this equation, we get the 95% confidence interval for the population mean to be:
(76.53, 84.47)
Therefore, we can say with 95% confidence that the true population mean lies between 76.53 and 84.47.
Step-by-step explanation:
correct me if i'm wrong po