A survey asked how many colleges students applied to, and 26 students responded to this question (based on simple random sampling, no extreme skew). This sample yielded an average of 9.7 college applications with a standard deviation of 7. The College Board website states that counselors recommend students apply to roughly 8 colleges.

Do these data provide convincing evidence that the average number of colleges all students apply to is different than recommended? Conduct a two-tailed t-test with the significance level of 5%. Include the full calculation in your answer and interpret the results.