Question

A random sample of 80 eighth grade​ students' scores on a national mathematics assessment test paper has a mean score of 269. This test result prompts a state school administrator to declare that the mean score for the​ state's eighth graders on this paper is more than 260 Assume that the population standard deviation is 31. At alphaαequals=0.06 is there enough evidence to support the​ administrator's claim? Complete parts​ (a) through​ (e).

​(a) Write the claim mathematically and identify Upper H 0H0 and Upper H Subscript aHa.

​(b) Find the standardized test statistic​ z, and its corresponding area.

​(c) Find the​ P-value.

​(d) Decide whether to reject or fail to reject the null hypothesis.

​(e) Interpret your decision in the context of the original claim.

At the 6​% significance​ level, there (Blank) enough evidence to Blank the​ administrator's claim that the mean score for the​ state's eighth graders on the paper is more than 260.

Answer 1

Here we have given that,

Xi: Grade student's score on a national mathematics test

n= Number of students=80

= sample mean = 269   

= Population standard deviation= 31

Here the population standard deviation is known we are using the one-sample z-test to test the hypothesis.

(a)

Claim: To check whether the population mean score fo the state's eighth readers on the paper is more than 260.

The null and alternative hypothesis is as follows

Versus

where, = population mean score for the state's eighth readers on the paper

This is the right one-tailed test.

(B)

Now, we can find the test statistic

z-statistics =

                  =

                  = 2.60

The Test statistic is 2.60

(C)

Now we can find the P-value

P-value = P(Z > z-statistics)) as this is right one tailed test

               =1- P( Z < 2.60)

=1 - 0.99534 Using standard normal z table see the value corresponding to the z=2.60

                =0.0047

we get the P-value is 0.0047

(D)

Decision:

= level of significance=6%=0.06

P-value (0.0047) less than (<)  0.06 ()

Conclusion

we reject Ho (Null Hypothesis)

At the 6​% significance​ level, there is enough evidence to Blank the​ administrator's claim that the mean score for the​ state's eighth-graders on the paper is more than 260