Question

A random sample of students was selected to take a reading assessment. There were 78 students in the sample which produced a mean score of 282 with a standard deviation of 35. This set of results prompted the state officials to declare that the true mean score on the test is less than 275. Calculate the p-value for the test and determine if the state officials were correct in their claim.

Answer 1

i am using minitab to solve the problem.

steps :-

copy the data in minitab and name the column x $1596051930854_blob.png$ stat $1596051930978_blob.png$ basic statistics $1596051930897_blob.png$ 1-sample T $1596051930881_blob.png$ select summarized data from the drop down menu $1596051930866_blob.png$ type 78 in sample size, 282 in sample mean,35 in standard deviation  $1596051931005_blob.png$tick perform hypothesized test $1596051930882_blob.png$in hypothesized mean type 275$1596051930906_blob.png$options $1596051930917_blob.png$ in confidence level type 95 $1596051930883_blob.png$ select alternative hypothesis as mean < hypothesized mean $1596051931066_blob.png$ok$1596051931005_blob.png$ok.

the minitab output be:-

Test

Null hypothesis	H₀: μ = 275
Alternative hypothesis	H₁: μ < 275

T-Value	P-Value
1.77	0.959

*** SOLUTION ***

p value = 0.959

decision:-

p value = 0.959 >0.05 (alpha)

we fail to reject the null hypothesis. There is not enough evidence that the state officials were correct in their claim.

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