To test whether the NCL's claim is true, we will use a one-sample t-test.
Null Hypothesis (H0): The average age of grandmasters is 55.
Alternative Hypothesis (H1): The average age of grandmasters is not equal to 55.
We will use a significance level of 1%.
Given that the sample mean (x̄) is 59.18 and the sample variance (s^2) is 168.60, we can calculate the standard error (SE) using the formula:
SE = sqrt(s^2/n)
Where n is the sample size. In this case, n = 50.
SE = sqrt(168.60/50) = sqrt(3.372) = 1.836
Next, we need to calculate the t-statistic using the formula:
t = (x̄ - μ) / (SE)
Where μ is the mean under the null hypothesis. In this case, μ = 55.
t = (59.18 - 55) / 1.836 = 2.38
Finally, we compare the t-statistic to the critical value from the t-distribution table. Since we're conducting a two-tailed test, we need to divide the significance level (1%) by 2 to get 0.5%.
df = n - 1 = 50 - 1 = 49
Critical value = ±2.675 (from t-distribution table with 0.5% significance level and 49 degrees of freedom)
Since the calculated t-statistic (2.38) does not exceed the critical value (±2.675), we fail to reject the null hypothesis. There is not enough evidence to support the claim that the average age of grandmasters is not equal to 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.
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