Question

How do California high school students compare to students nationwide in their college readiness, as measured by their SAT scores? The national average scores for the class of 2017 were 533 on Evidence-Based Reading and Writing and 527 on the math portion.† Suppose that 100 California students from the class of 2017 were randomly selected and their SAT scores were recorded in the following table.

	Evidence-Based Reading and Writing	Math
Sample Average	529	521
Sample Standard Deviation	96	99

(a)

Do the data provide sufficient evidence to indicate that the average Evidence-Based Reading and Writing score for all California students in the class of 2017 differs from the national average? Use α = 0.05.

State the null and alternative hypotheses.

H₀: μ < 527 versus H_a: μ > 527

H₀: μ = 533 versus H_a: μ > 533     

H₀: μ = 533 versus H_a: μ ≠ 533

H₀: μ = 533 versus H_a: μ < 533

H₀: μ ≠ 527 versus H_a: μ = 527

Find the test statistic and the p-value. (Round your test statistic to two decimal places and your p-value to four decimal places.)

z=

p-value =

State your conclusion.

The p-value is less than alpha, so H₀ is rejected. There is sufficient evidence to indicate that the average Evidence-Based Reading and Writing score for all California students in the class of 2017 is different from the national average.

The p-value is greater than alpha, so H₀ is not rejected. There is sufficient evidence to indicate that the average Evidence-Based Reading and Writing score for all California students in the class of 2017 is different from the national average.    

The p-value is greater than alpha, so H₀ is not rejected. There is insufficient evidence to indicate that the average Evidence-Based Reading and Writing score for all California students in the class of 2017 is different from the national average.

The p-value is less than alpha, so H₀ is rejected. There is insufficient evidence to indicate that the average Evidence-Based Reading and Writing score for all California students in the class of 2017 is different from the national average.

(b)

Do the data provide sufficient evidence to indicate that the average math score for all California students in the class of 2017 is different from the national average? Use α = 0.05.

State the null and alternative hypotheses.

H₀: μ < 527 versus H_a: μ > 527

H₀: μ = 533 versus H_a: μ > 533   

  H₀: μ ≠ 527 versus H_a: μ = 527

H₀: μ = 533 versus H_a: μ < 533

H₀: μ = 527 versus H_a: μ ≠ 527

Find the test statistic and the p-value. (Round your test statistic to two decimal places and your p-value to four decimal places.)

z=

p-value =

State your conclusion.

The p-value is greater than alpha, so H₀ is not rejected. There is insufficient evidence to indicate that the average math score for all California students in the class of 2017 is different from the national average.

The p-value is less than alpha, so H₀ is rejected. There is sufficient evidence to indicate that the average math score for all California students in the class of 2017 is different from the national average.     

The p-value is greater than alpha, so H₀ is not rejected. There is sufficient evidence to indicate that the average math score for all California students in the class of 2017 is different from the national average.

The p-value is less than alpha, so H₀ is rejected. There is insufficient evidence to indicate that the average math score for all California students in the class of 2017 is different from the national average.

Answer 1

a)

H₀: μ = 533 versus H_a: μ ≠ 533

........
          
Level of Significance ,    α =    0.050  
sample std dev ,    s =    96.0000  
Sample Size ,   n =    100  
Sample Mean,    x̅ =   529.0000  
          
degree of freedom=   DF=n-1=   99  
          
Standard Error , SE = s/√n =   96/√100=   9.6000  
t-test statistic= (x̅ - µ )/SE =    (529-533)/9.6=   -0.42  
          

          
p-Value   =   0.6778   [Excel formula =t.dist(t-stat,df) ]
The p-value is greater than alpha, so H₀ is not rejected. There is insufficient evidence to indicate that the average Evidence-Based Reading and Writing score for all California students in the class of 2017 is different from the national average.

...................

b)

Ho :   µ =   527  
Ha :   µ ╪   527  
          
Level of Significance ,    α =    0.050  
sample std dev ,    s =    99.0000  
Sample Size ,   n =    100  
Sample Mean,    x̅ =   521.0000  
          
degree of freedom=   DF=n-1=   99  
          
Standard Error , SE = s/√n =   99/√100=   9.9000  
t-test statistic= (x̅ - µ )/SE =    (521-527)/9.9=   -0.61  
          
          
p-Value   =   0.5459   [Excel formula =t.dist(t-stat,df) ]

The p-value is greater than alpha, so H₀ is not rejected. There is insufficient evidence to indicate that the average math score for all California students in the class of 2017 is different from the national average.

...............

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