(Solved): 7. Samples were taken from two schools regarding students' allowances. A sample from 25 students f ...

7. Samples were taken from two schools regarding students' allowances. A sample from 25 students from School X revealed an average allowance of $200 per week with a standard deviation of $15. Meanwhile, a sample from 35 students from School Y revealed an average of $180 per week with a standard deviation of $20. Consider a 5% level of significance. Test the hypothesis that students from School X have a higher allowance compared to School B and identify the appropriate test statistic. t=4.425 t=4.220 z=4.425 Z=4.245 8. From 20 applicants consisting of 12 woodwind musicians and 8 brass musicians, the conductor will select 7 members who will join the ensemble. If every applicant has an equal and independent chance of being chosen, what is the probability of choosing 5 woodwind musicians? 0.6396 0.0477 0.8485 0.2861 9. Which of the following is true about the relationship between sample size, margin of error, and confidence interval using the t-distribution? A larger sample allows for a smaller margin of error which results in a wider confidence interval. A larger sample allows for a smaller margin of error which results in a narrower confidence interval. A smaller sample allows for a larger margin of error which results in a narrower confidence interval. A smaller sample allows for a smaller margin of error which results in a wider confidence interval. 10. A 6-sided die is biased in such a way that the probability of a "six" appearing on top is 20% and all other possibilities have an equal chance of appearing on top. If the die is thrown 5 times, what is the probability that a "six" will appear at most 3 times? 0.0026 0.0080 0.9974 0.9920