Complete Question
The complete question is shown on the first uploaded image
Answer:
The 95% confidence interval is
The test statistics is
The p-value is
The <u>p-value</u> suggests that the null hypothesis is<u> rejected </u>with a high degree of confidence. Hence <u>there is</u> statistically significant evidence that the districts with smaller classes have higher average test score
Step-by-step explanation:
From the question we are told that
The sample size is n = 408
The sample mean is
The standard deviation is
Given that the confidence level is 95% then the level of significance is
From the normal distribution table the critical value of is
Generally the margin of error is mathematically represented as
=>
=>
Generally the 95% confidence interval is mathematically represented as
=>
=>
=>
From the question we are told that
Class size small large
sample size
The null hypothesis is
The alternative hypothesis is
Generally the standard error for the difference in mean is mathematically represented as
=>
=>
Generally the test statistics is mathematically represented as
=>
=>
Generally the p-value is mathematically represented as
From the z-table
So
From the values we obtained and calculated we can see that
This mean that
The p-value suggests that the null hypothesis is rejected with a high degree of confidence. Hence there is statistically significant evidence that the districts with smaller classes have higher average test score
