Answer:
Step-by-step explanation:
The mean of the set of data given is
Mean = (275.4 + 276.8 + 273.9 + 275.0 + 275.8 + 275.9 + 276.1)/7 = 275.56
Standard deviation = √(summation(x - mean)^2/n
n = 7
Summation(x - mean)^2 = (275.4 - 275.56)^2 + (276.8 - 275.56)^2 + (273.9 - 275.56)^2 + (275.0 - 275.56)^2 + (275.8 - 275.56)^2 + (275.9 - 275.56)^2 + (276.1 - 275.56)^2 = 5.0972
Standard deviation = √(5.0972/7) = 0.85
We would set up the hypothesis test.
For the null hypothesis,
µ = 275
For the alternative hypothesis,
µ ≠ 275
This is a 2 tailed test.
Since the number of samples is small and no population standard deviation is given, the distribution is a student's t.
Since n = 7
Degrees of freedom, df = n - 1 = 7 - 1 = 6
t = (x - µ)/(s/√n)
Where
x = sample mean = 275.56
µ = population mean = 275
s = samples standard deviation = 0.85
t = (275.56 - 275)/(0.85/√7) = 1.74
We would determine the p value using the t test calculator. It becomes
p = 0.132
Because the p-value of 0.132 is greater than the significance level of 0.05, we would fail to reject the null hypothesis. We conclude the data does not provide convincing evidence that the mean amount of juice in all the bottles filled that day differs from the target value of 275 milliliters.
