Answer:
Step-by-step explanation:
The mean of the set of data given is
Mean = (60 + 120 + 110 + 80 + 70 + 90 + 100 + 130)/8 = 95
Standard deviation = √(summation(x - mean)/n
n = 8
Summation(x - mean) = (60 - 95)^2 + (120 - 95)^2 + (110 - 95)^2 + (80 - 95)^2 + (70 - 95)^2 + (90 - 95)^2 + (100 - 95)^2 + (130 - 95)^2 = 4200
Standard deviation = √(4200/8) = 22.91
We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean
For the null hypothesis,
µ ≤ 120
For the alternative hypothesis,
µ > 120
This is a right 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 = 8,
Degrees of freedom, df = n - 1 = 8 - 1 = 7
t = (x - µ)/(s/√n)
Where
x = sample mean = 95
µ = population mean = 120
s = samples standard deviation = 22.91
t = (95 - 120)/(22.91/√8) = - 3.09
We would determine the p value using the t test calculator. It becomes
p = 0.009
Since alpha, 0.05 > than the p value, 0.009, then we would reject the null hypothesis. Therefore, At a 5% level of significance, the sample data showed significant evidence that the average seven-year-old would be able to swim across an Olympic-sized pool in more than 120 seconds after taking lessons from their instructors.
