To test whether the NCL's claim is true, we can set up the following hypotheses:
Null Hypothesis (H₀): The average age of a grandmaster is 55 (μ = 55)
Alternative Hypothesis (H₁): The average age of a grandmaster is not 55 (μ ≠ 55)
To test this, we can use a t-test since we have the sample mean and variance.
The test statistic for a t-test is calculated as:
t = (sample_mean - population_mean) / (sample_standard_deviation / sqrt(sample_size))
First, let's calculate the sample standard deviation:
sample_standard_deviation = sqrt(sample_variance)
= sqrt(168.60)
= 12.99
Now, we can calculate the test statistic:
t = (59.18 - 55) / (12.99 / sqrt(50))
= 4.18 / (12.99 / 7.07)
= 4.18 / 1.839
= 2.27
Next, we need to find the critical value for a 1% level of significance. Since this is a two-tailed test, we divide the significance level by 2 and look up the corresponding value in the t-distribution table. Using a table or statistical software, we find that the critical value for a 1% level of significance with a sample size of 50 is approximately 2.68.
Since the test statistic (2.27) is less than the critical value (2.68), we do not reject the null hypothesis.
Therefore, we do not have enough evidence to conclude that the average age of grandmasters is different from 55 at a 1% level of significance.
The ages of competitors in a grandmaster chess tournament is under dispute. The National Chess League (NCL) claims that the average age of a grandmaster is 55. A random sample of 50 competitors at a recent tournament resulted in a mean of 59,18 and a variance of 168,60. Test at a 1% level of significance whether the NCL's claim is true.
1 answer
1 answer