Respuesta :
Answer:
Step-by-step explanation:
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,
H0: µ = 305
For the alternative hypothesis,
H1: µ > 305
This is a right tailed test
Since the population standard deviation is given, z score would be determined from the normal distribution table. The formula is
z = (x - µ)/(σ/√n)
Where
x = sample mean
µ = population mean
σ = population standard deviation
n = number of samples
From the information given,
µ = 305
x = 306.2
σ = 3.57
n = 55
z = (306.2 - 305)/(3.57/√55) = 2.49
Test statistic = 2.49
The calculated test statistic is 2.49 for the right tail and - 2.49 for the left tail
Since α = 0.05, the critical value is determined from the normal distribution table.
For the left, α/2 = 0.05/2 = 0.025
The z score for an area to the left of 0.025 is - 1.96
For the right, α/2 = 1 - 0.025 = 0.975
The z score for an area to the right of 0.975 is 1.96
In order to reject the null hypothesis, the test statistic must be smaller than - 1.96 or greater than 1.96
Since - 2.49 < - 1.96 and 2.49 > 1.96, we would reject the null hypothesis.
Therefore, at 5% level of significance, there is sufficient evidence to conclude that the average depth has increased.
