Question

11. High School Standardized Test Past experience indicates that the time required for high school seniors to complete a standardized test is a normal random variable with a mean of 35 minutes (normally distributed). If a random sample of 30 high school seniors took an average of 33.5 minutes to complete this test with a standard deviation of 4 minutes, test the hypothesis, at the 0.05 level of significance, that u = 35 minutes against the alternative that u <35 minutes.

a. Parameter of Interest

b. Null and Alternative hypothesis

c. Test Statistic

d. Reject Ho if

e. Computations

f. Conclusions

Answer 1

given data are:-

sample size (n) = 30

sample mean () = 33.5

sample sd (s) = 4

a).parameter of interest:-

the true population mean () time required for high school seniors to complete a standardized test.

b).null and alternative hypothesis:-

c).test statistic be:-

d).reject H₀, if p value < 0.05 (alpha)

e).degrees of freedom = (n-1)= (30-1) = 29

the p value is :-

[ in any blank cell of excel type =T.DIST(-2.054,29,TRUE)]

f).conclusion:-

p value = 0.0245 < 0.05 (alpha)

we reject the null hypothesis and conclude that the time required for high school seniors to complete a standardized test is less than 35 minutes.

*** if you have any doubt regarding the problem ,please write it in the comment box...if satisfied,please UPVOTE.