The human resources department of an engineering company gives IQ tests to a randomly selected group of new hires every year. They claimed that the mean IQ score of new hires, , from this year is greater than or equal to the mean IQ score of new hires, , from last year. This year, new hires took the test and scored an average of points with a standard deviation of . Last year, new hires took the IQ test and they scored an average of points with a standard deviation of . Assume that the population standard deviation of the IQ scores from the current year and the last year can be estimated by the sample standard deviations, since the samples that are used to compute them are quite large. Is there enough evidence to reject the claim of the human resources department, at the level of significance? Perform a one-tailed test. Then fill in the table below.

Question

The human resources department of an engineering company gives IQ tests to a randomly selected group of new hires every year. They claimed that the mean IQ score of new hires, , from this year is greater than or equal to the mean IQ score of new hires, , from last year. This year,  new hires took the test and scored an average of  points with a standard deviation of . Last year,  new hires took the IQ test and they scored an average of points with a standard deviation of . Assume that the population standard deviation of the IQ scores from the current year and the last year can be estimated by the sample standard deviations, since the samples that are used to compute them are quite large. Is there enough evidence to reject the claim of the human resources department, at the  level of significance? Perform a one-tailed test. Then fill in the table below.

PsyDAG · Answer

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Explain Bot · Answer

To determine if there is enough evidence to reject the claim of the human resources department, we can conduct a hypothesis test using the provided information. Let's set up the null and alternative hypotheses: Null Hypothesis (H0): The mean IQ score of new hires from this year is less than or equal to the mean IQ score of new hires from last year. µ1 ≤ µ2 Alternative Hypothesis (Ha): The mean IQ score of new hires from this year is greater than the mean IQ score of new hires from last year. µ1 > µ2 (Note: µ1 is the mean IQ score of new hires from this year, and µ2 is the mean IQ score of new hires from last year.) Next, we need to calculate the test statistic. In this case, the appropriate test statistic to use is the independent samples t-test, since we have two independent samples and want to compare their means. The formula for the t-test statistic is: t = (x1 - x2) / √((s1^2 / n1) + (s2^2 / n2)) Where: x1 = average IQ score of new hires from this year x2 = average IQ score of new hires from last year s1 = standard deviation of the IQ scores from this year's sample s2 = standard deviation of the IQ scores from last year's sample n1 = number of new hires this year n2 = number of new hires last year Given values: x1 = average of points = ? x2 = average of points = ? s1 = standard deviation of = ? s2 = standard deviation of = ? n1 = number of new hires this year = ? n2 = number of new hires last year = ? Unfortunately, the actual values for x1, x2, s1, s2, n1, and n2 are missing in the question. Please provide those missing values, so that we can calculate the test statistic and perform the hypothesis test.