Question

A random sample of 60 second graders in a certain school district are given a standardized mathematics skills test. The sample mean score is = 52. Assume the standard deviation of test scores is σ = 15. The nationwide average score on this test is 50. The school superintendent wants to know whether the second graders in her school district have greater math skills than the

nationwide average.
a) State the appropriate null and alternate hypotheses.b) Compute the P-Value.

Answer 1

a) Null hypothesis:
`\mu \leq 50`

Alternative hypothesis:
`\mu > 50`

b)
`z=(52-50)/((15)/(√(60)))=1.033`

`p_v =P(z>1.033)=0.1508`

Explanation:

Information suministred

`\bar X=52` represent the sample mean score for the econd graders

`\sigma=15` represent the population standard deviation

`n=60` sample size

`\mu_o =50` represent the value that we want to test

z would represent the statistic

`p_v` represent the p value for the test (variable of interest)

Part a: System of hypothesis

We want to check if the second graders in her school district have greater math skills than the nationwide average, the system of hypothesis would be:

Null hypothesis:
`\mu \leq 50`

Alternative hypothesis:
`\mu > 50`

Part b

The statistic is given by:

`z=(\bar X-\mu_o)/((\sigma)/(√(n)))` (1)

Replacing into the formula we got:

`z=(52-50)/((15)/(√(60)))=1.033`

We have a right tailed test then the p value would be:

`p_v =P(z>1.033)=0.1508`