Hi Linda,
The question is asking you to run a significance test to figure out if the results of the study differ significantly enough from the population value to determine if the test demonstrates a high probability that the population value is either wrong or has changed.
The null hypothesis (H0) says that the test did not show a significant enough difference from the predicted value, and so the original value is likely still true.
The alternative hypothesis (H1) says that the test value differs significantly enough from the predicted value that the predicted value is likely false.
The cutoff for the significance test is at 1.96 standard deviations from the population mean. This means that if the test value is less than or equal to -1.96 or greater than or equal to 1.96 standard deviations from the mean, the result would be considered significant.
H0 will be rejected, and H1 will be accepted if
-1.96 ≥ Z
or
Z ≥ 1.96
Since we know the population mean is 30 and with a standard deviation of 5, we just have to multiply the number of standard deviations that we care about by the standard deviation (5) and then add and subtract that value from the mean to find the upper and lower limits, respectively.
5 * 1.96 = 9.8
30 ±9.8
Reject H0 if the test value is in the interval (-∞,-20.2] ∪ [39.8,∞)
The test value is 45, which is in the interval (-∞,-20.2] ∪ [39.8,∞), therefore the test value differs from the predicted value significantly enough to reject the null hypethesis.
I hope that helps!
