A social psychologist wants to know whether students' performance on a problem solving task is lowered by having other people look on when completing the task. She randomly selects 21 students and has them complete the task with onlookers and finds that their mean score on the problem solving task equals 89.8 with variance equal to 84.6. Scores on the problem solving task for the population of students who complete the task without onlookers are distributed normally with a mean equal to 89.1. Is there sufficient evidence to conclude that performance on the problem solving task is lowered by having onlookers

Yes, there is sufficient evidence to conclude that performance on the problem solving task is lowered by having onlookers.

Step-by-step explanation:

Null hypothesis: The performance on the problem solving task is lowered by having onlookers.

Alternate hypothesis: The performance on the problem solving task is not lowered by having onlookers.

Test statistic (t) = (sample mean - population mean) : (sample sd/√n)

sample mean = 89.8

population mean = 89.1

sample sd = √sample variance = √84.6 = 9.198

n = 21

Degree of freedom = n-1 = 21-1 = 20

Assuming a 5% significance level

The test is a two-tailed test. Critical values corresponding to 20 degrees of freedom and 5% significance level are - 2.086 and 2.086

Test statistic (t) = (89.8 - 89.1) : (9.198/√21) = 0.7 : 2.007 = 0.349

Conclusion:

Fail to reject the null hypothesis because the test statistic 0.349 falls within the region bounded by the critical values.

There is sufficient evidence to conclude that performance on the problem solving task is lowered by having onlookers.