You conduct a survey of a sample of 25 members of this year’s graduating marketing students and find that the average GPA is 3.2. The standard deviation of the sample is 0.4. Over the last 10 years, the average GPA has been 3.0. Is the GPA of this year’s students significantly different from the long-run average? At what alpha level would it be significant
What are some of the different stages that a company goes through when developing their IMC strategy
To determine whether the GPA of this year's students is significantly different from the long-run average, we will perform a hypothesis test using a t-test.
The hypothesis test involves comparing two hypotheses:
Null hypothesis (H0): The average GPA of this year's students is equal to the long-run average (μ = 3.0).
Alternative hypothesis (Ha): The average GPA of this year's students is significantly different from the long-run average (μ ≠ 3.0).
To conduct the t-test, we calculate the test statistic using the formula:
t = (sample mean - population mean) / (standard deviation / square root of sample size)
In this case, the sample mean is 3.2, the population mean is 3.0, the standard deviation is 0.4, and the sample size is 25.
t = (3.2 - 3.0) / (0.4 / √25)
t = 0.2 / (0.4 / 5)
t = 0.2 / 0.08
t = 2.5
Next, we compare the obtained test statistic (t = 2.5) with the critical values from the t-distribution table for the corresponding significance level. This significance level is usually denoted as α (alpha).
To determine the alpha level at which the test would be significant, we need to select a desired level of significance. Commonly used levels of significance are 0.05 (5%) and 0.01 (1%).
For example, if we choose a significance level of 0.05, we need to find the critical t-value with a degrees of freedom of n - 1 (25 - 1 = 24) that corresponds to an area of 0.025 in both tails of the distribution. In a two-tailed test, we divide the significance level by 2 (0.05 / 2 = 0.025) and find the critical t-value.
Once we have the critical t-value, we compare it with the obtained test statistic. If the obtained test statistic is greater than the critical t-value (in the rejection region), we reject the null hypothesis and conclude that the GPA of this year's students is significantly different from the long-run average.
Calculating the critical t-value and determining the significance level at which the test would be significant requires referring to a t-distribution table or using statistical software.
Note: This is a general explanation of how to conduct the hypothesis test. The actual critical t-value and significance level may differ based on the degrees of freedom and chosen alpha level.