5.22 High School and beyond, Part II We considered the differences between the r

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5.22 High School and beyond, Part II We considered the differences between the reading and writing scores of a random sample of 200 stuidents who took the High School and Beyond Survey in Exercise 5.21. The mean and standard deviation of the differences are Xread.write0.545 and S.887 points respectively (a) Calculate a 95% confidence interval for the average difference between the reading and writing scores of all students. lower bound upper bound points plsare round to two decimal places) points please round to nsa decimal piaces b) Interpret this interval in context. 95% of students will have a difference between reading and writing scores that falls within our confidence moral we can be 95% confident that the average difference between reading and writing scores of all students is contained within our confidence interval we can be 95% confident that our confidence interval contains the mean difference between reading and writing scores afthese 200 students c) Does thc confidence interval provide coavincing evidence that there is arcal difference in the average scores? Explain no, since 0 is contained in our confidence interval no, because or confidence interval contains both positive and negative values ves, because ne yes, since0 is contained in aur confidence interval Box 1:Enter your answer as an integer or decimal number. Examplcs: 3,-4, 5.5172 Enter DNE for Docs Not Exist, oo for Infinity Box 2: Enter yoour answer as an integer or decimal number. Examples: 3. -4, 5.3172 Enter DNE for Daes Not Exist, oo for Infinity Box 3 Select the best awer Box 4: Sclect the best answer Activate Windows

Explanation / Answer

Question 5.22

Solution:

We are given

Part a

Confidence interval = Dbar -/+ t*Sd/sqrt(n)

We are given

Dbar = 0.545

Sd = 8.887

n = 200

Confidence level = 95%

Degrees of freedom = n – 1 = 200 – 1 = 199

Critical t value = 1.9720

(By using t-table or excel)

Confidence interval = 0.545 -/+ 1.9720*8.887/sqrt(200)

Confidence interval = 0.545 -/+ 1.9720* 0.628405796

Confidence interval = 0.545 -/+ 1.2392

Lower limit = 0.545 - 1.2392 = -0.6942

Upper limit = 0.545 + 1.2392 = 1.7842

Confidence interval = (-0.6942, 1.7842)

Lower limit = -0.69

Upper limit = 1.78

Part b

Interpretation:

We can 95% confident that the average difference between reading and writing scores of all students is contained within our confidence interval.

(We know that the confidence interval is associated with population parameter. Here, confidence interval is associated with the average difference between reading and writing scores of all students.)

Part c

Answer:

No, since 0 is contained in our confidence interval.

(We know that if the value of difference 0 is lies within confidence interval, then we do not reject the null hypothesis that there is no real difference in the average scores.)

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