To test whether the new class of students is significantly more intelligent than the school's overall student body, a one-sample t-test can be used. The test statistic is calculated using the formula: t = (sample mean - population mean) / (standard deviation / sqrt(sample size)). The new class's mean IQ can be compared to the critical value at a chosen significance level to determine statistical significance.
To test whether the new class of students is significantly more intelligent than the school's overall student body, we can use a one-sample t-test. The null hypothesis for this test is that there is no significant difference in mean IQ between the new class and the school's overall student body. The alternative hypothesis is that the mean IQ of the new class is significantly higher than the school's overall student body.
We can calculate the test statistic using the formula:
t = (sample mean - population mean) / (standard deviation / sqrt(sample size))
Using the given information, we have:
sample mean = 134
population mean = 127
standard deviation = 8
sample size = 32
Calculating the test statistic:
t = (134 - 127) / (8 / sqrt(32)) = 2.83
To determine whether this test statistic is statistically significant, we need to compare it to the critical value at a chosen significance level (e.g., 0.05). If the test statistic is greater than the critical value, we can reject the null hypothesis and conclude that the new class has a significantly higher mean IQ than the school's overall student body.