Answer:
The 96% confidence interval for the mean number of ounces of ketchup per bottle in the sample is 24 ± 0.029
Step-by-step explanation:
Given
Mean, x = 24 ounces
Standard deviation, σ = 0.2 ounces
Sample Size, n = 49 bottles of ketchup
Confidence Interval of 95% (0.95)
To calculate the confidence at this level, the following steps are to be followed;
1. Calculating degree of freedom:
Degree of freedom (df) is calculated by subtracting 1 from the sample size.
df = n - 1
df = 49 - 1
df = 48
2. Subtract the confidence level from 1, then divide by two.
α = (1 – .95) / 2 = 0.025
3. Look up the answers to (1) and (2) in the t-distribution table.
For 48 degrees of freedom (df) and α = 0.025,
We get 2.0106
4. Divide sample standard deviation by the square root of sample size.
i.e σ/√n
= 0.2/√49
= 0.2/7
= 0.02857
= 0.029
5. Finally, the 95% confidence interval is calculated using the following illustration.
X ± result in step 5
Where x = 24
So, we have
24 ± 0.029
