The likely average time to graduate, considering the provided percentages and years, is calculated to be 5 years. To statistically verify this at the 1 percent significance level, a one-sample t-test can be conducted using the provided sample data.
To determine the likely average time to graduate, we need to examine the statistics provided and calculate a weighted average based on the percentages and the corresponding years to graduate. Using the percentages 40%, 30%, 20%, and 10% and the numbers of years 4, 5, 6, and 7, respectively, the likely average can be found through the following calculation:
0.40 (4 years) = 1.6
0.30 (5 years) = 1.5
0.20 (6 years) = 1.2
0.10 (7 years) = 0.7
Adding these products together, we obtain:
1.6 + 1.5 + 1.2 + 0.7 = 5 years
Thus, the likely average time to graduate is 5 years.
If we want to assess whether the sample mean of students from SCSU supports that the average time to graduate is more than the California state university system average of 4.5 years at the 1 percent level, we have to perform a hypothesis test, specifically a one-sample t-test, given that we have the sample size (n = 49), the sample mean (5.1 years), and the sample standard deviation (1.2 years).