sample of 82 eighth grade students\' scores on a national mathematics assessment

Question

sample of 82 eighth grade students' scores on a national mathematics assessment test has a mean score of 277, This test result prompts a state school to declare that the mean score for the state's eighth graders on this exam is more than 275. Assume that the population standard deviation is 35 A 04, is there enough evidence to (b) Find the standardized test statistic z, and its corresponding area 52(Round to two decimal places as needed) (c) Find the P-value P-value 1.397 (Round to three decimal places as needed) (d) Decide whether to reject or fail to reject the null hypothesis Click to select your answer(s

Explanation / Answer

The null hypothesis here is

Ho: mean score mu= 275

& the alternative hypothesis is

H1: mean score mu> 275

So it's a one tail test since we are checking for the mu>275

so here we have to use the formula as

Z= (X'-mu)/ (sd/sqrt(n)) to calculate the critical value of Z and find the p value accordingly from z

so., we have X'=277,mu=275,sd=35,n=82

so., z=(277-275)/(35/sqrt(82))=0.52 (you made a mistake by taking X' as mu and mu as X' since we are given a sample mean as 277 and population mean as 275 since they are claiming the population mean > 275 and always remember the population is under test and not sample)

checking the p value at z value = 0.52 in the z table we get p=0.6975792 but since it's an upper tail test the p value becomes the right side area of the curve and from z table we got the area = 0.6975792 as the area towards left and so the actual p value here = 1-0.6975792=0.3024208

since we are checking the hypothesis at 4% or 0.04 significance the p value here calculated is 0.3024208 which is not less than 0.04 and so we cannot reject the null hypothesis

So ultimately we are saying that the claim of the population mean > 275 is false at 4% significance level. (if you dig deeper then even higher sd of 35 and small sample size of 82 itself makes claim paltry)  

Hope the above explaination has helped you in understanding the problem Pls upvote the ans if it has really helped you. Good Luck!!

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