Question

A teacher believes that the standard deviation of scores for a particular test that he gives every semester is 4 points.
His current students claim that the standard deviation is more than 4 points.
L​et σ2 be the true variance for the test scores.
A​ random sample of 10 test scores from the current semester has an observed standard deviation of s=5.2 points.
Assuming that test scores are normally distributed, c​onsider testing the hypotheses
H0:σ2 = 16 versus H1:σ2>16.
G​ive the P-value for the appropriate test, rounded to 3 decimal places.

Answer 1

As per the given standard deviation, the p - value is 0.09997

The term standard deviation means a number that represents the "spread" or "dispersion" of a set of data and there are other measures for spread, such as range and variance.

Here we have given that teacher believes that the standard deviation of scores for a particular test that he gives every semester is 4 points. His current students claim that the standard deviation is more than 4 points. Let σ2 be the true variance for the test scores.

Here we need to find the P-value for the appropriate test, rounded to 3 decimal places.

While we looking into the given question we have identified the values of the following

Standard deviation = 5.2

H0 : σ² = 16 

H1 : σ² > 16.

Now, we have to calculate the value of z as,

Let us consider that the significance level as 0.05, then the critical value of z is,

Critical value (1-tailed) = 1.645.

Then the p - value is calculated as,

Based on the critical value, the P-Value is .09997.

And the result is not significant at p < .05.

To know more about Standard deviation here.

https://brainly.com/question/16555520

#SPJ4