At the 0.01 significance level, we do not have sufficient evidence to conclude that parents read more than the average number of books to their children.
How to determine whether parents read more than the average number of books to their children
To determine whether parents read more than the average number of books to their children, conduct a hypothesis test using the given information.
Set up the hypotheses:
Null Hypothesis (H0): The mean number of books read per month by parents is equal to the population mean (μ = 10).
Alternative Hypothesis (H1): The mean number of books read per month by parents is greater than the population mean (μ > 10).
Use a one-sample t-test since the population standard deviation is unknown, and the sample size is relatively small (n = 25).
Given:
Sample mean (x) = 12
Population standard deviation (σ) = 5
Sample size (n) = 25
Significance level (α) = 0.01 (or 1% level of significance)
Next, calculate the test statistic (t-score) using the formula:
t = (x - μ) / (σ /
(n))
Substituting the given values:
t = (12 - 10) / (5 /
(25))
t = 2 / (5 / 5)
t = 2
To determine the critical value, look up the t-value corresponding to the significance level and degrees of freedom (df = n - 1). Since the sample size is 25, the degrees of freedom is 25 - 1 = 24.
Using a t-table or statistical software, we find that the critical t-value for a one-tailed test with a significance level of 0.01 and 24 degrees of freedom is approximately 2.492.
Since the calculated t-value (t = 2) is less than the critical t-value (2.492), we fail to reject the null hypothesis.
Therefore, at the 0.01 significance level, we do not have sufficient evidence to conclude that parents read more than the average number of books to their children.