question archive 1) Suppose a tutoring company advertises that its clientele average 80% in their math courses
1) Suppose a tutoring company advertises that its clientele average 80% in their math courses
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1) Suppose a tutoring company advertises that its clientele average 80% in their math courses. Feeling skeptical, you question a sample of 9 students who used the tutoring service, finding that their average was only 68%, with a standard deviation of 11%:
(a) State the null and alternative hypotheses, H0 and H1 :
(b) Calculate the appropriate t−statistic at the 5% significance level:
(c) Estimate the p−value, and describe what it means in the context of this problem:
(d) State your conclusions (ie: is the tutoring company necessarily not being truthful? Why would we observe an average of 68% when the stated average was so much greater? Share your thoughts):
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a. Ho: p = 0.80
H1: p =/ 0.80
(b) we use the t test formula
t = (p - po)/(sd/sqrt n)
t = (0.68 - 0.8)/(0.11 / sqrt 9)
t = -3.2727
(c) at df = n- 1 = 9-1 = 8 and t = -3.2727 is equal to 0.0056. This means that there is 0.56% probability that the clientele has a average of 80% in their math courses.
d. Since p value of 0.0056 is less than 0.05, we reject the null hypothesis and conclude that there is insufficient evidence to claim that the clientele has a average of 80% in their math courses. The difference in survey results can be attributed to small sample size. The larger the sample size, the closer the proportion to the population parameter, 0.80
