Identify the sample data as INDEPENDENT or DEPENDENT: An educator wants to determine if a tutoring program improves student test scores in math. A random sample of 30 students is given a pre-test and...



  1. Identify the sample data as INDEPENDENT or DEPENDENT:

  2. An educator wants to determine if a tutoring program improves student test scores in math. A random sample of 30 students is given a pre-test and then subjected to a month long tutoring program. At the end of the tutoring program the students take a post-test. The educator wants to do a hypothesis test to determine if the post-test scores are significantly better than the pre-test scores.











    INDEPENDENT
    DEPENDENT

    Question 2


  3. Identify the sample data as INDEPENDENT or DEPENDENT:

  4. The General Social Survey(GSS) polled a random sample of 209 people aged 18-30 in 2000 and asked them how many hours per week they spent on the Internet. The sample mean in 2000 was 6.75 hrs. In 2006, the GSS took another random sample of 541 people aged 18-30 and asked the same question. The sample mean in 2006 was 7.34. Does this mean that people aged 18-30 spend more time on the internet in 2006 than they did in 2000?









    INDEPENDENT
    DEPENDENT



    Question 3


  5. In a study of birth order and intelligence, IQ tests were given to 18- and 19- year old men to estimate the size of the difference, if any, between the mean IQs of firstborn sons and secondborn sons. The summary stats below show the mean and standard deviation of the IQ scores for the two groups.


  6. Summary statistics:





















    Column

    Mean

    Std. dev.
    Firstborn101.513.640218
    Secondborn102.49.1433036

    CHOOSE THE CORRECT HYPOTHESIS FOR THIS TEST. Let















    A.Ho:
    H1:
    B.Ho:
    H1:
    C.Ho:
    H1:



    Question 4


  7. In a study of birth order and intelligence, IQ tests were given to 18- and 19- year old men to estimate the size of the difference, if any, between the mean IQs of firstborn sons and secondborn sons. The summary stats below show the mean and standard deviation of the IQ scores for the two groups.


  8. Summary statistics:





















    Column

    Mean

    Std. dev.
    Firstborn101.513.640218
    Secondborn102.49.1433036


    Can you conclude that there is a difference in mean IQ between firstborn sons and secondborn sons?
    Let
    The output below shows the results of the appropriate hypothesis test, WHAT CAN YOU CONCLUDE BASED ON THESE RESULTS?

    Two sample T hypothesis test:

    µ1
    - µ2
    : Difference between two means
    H0
    : µ1
    - µ2
    = 0
    HA
    : µ1
    - µ2
    ? 0
    (without pooled variances)

    Hypothesis test results:






































    Difference

    Sample Diff.

    Std. Err.

    DF

    T-Stat

    P-value
    µ1
    - µ2
    		-0.95.192836915.729291-0.173315670.8646
    A.There is enough evidence of a difference in mean IQ between firstborn sons and secondborn sons
    B.There is not enough evidence of a difference in mean IQ between firstborn sons and secondborn sons .
    C.There is enough evidence that the mean IQ between firstborn sons and secondborn sons is the same.
    D.There is not enough evidence that the mean IQ between firstborn sons and secondborn sons is the same.

    2 points


    Question 5


  9. A new postsurgical treatment was compared with a standard treatment. Seven subjects received the new treatment, while seven others (the controls) received the standard treatment. The recovery times in days are given below:

  10. Treatment: 12 13 15 19 20 21 24
    Control: 18 23 24 30 32 32 39
    Can you conclude that the mean recovery time for those receiving the new treatment (population 1) is lower compared to the mean for those receiving the standard treatment (population 2)?
    CHOOSE THE CORRECT HYPOTHESIS FOR THIS TEST.















    A.Ho:
    H1:
    B.Ho:
    H1:
    C.Ho:
    H1:

    2 points


    Question 6


  11. The National Health Statistics Reports published in 2008 reported that a sample of 360 one-year-old boys had a mean weight of 25.5 lbs with a standard deviation of 5.3 pounds. In addition, a sample of 328 one-year-old girls had a mean weight of 24.1 pounds with a standard deviation of 4.3 pounds.

  12. The output below shows the 95% confidence interval comparing the difference in mean weights for one-year-old boys and girls.

    Two sample T confidence interval:

    µ1
    : Mean of Population 1 (boys)
    µ2
    : Mean of Population 2 (girls)
    µ1
    - µ2
    : Difference between two means

    95% confidence interval results:






















    Difference

    Sample Diff.

    Std. Err.

    DF

    L. Limit

    U. Limit
    µ1
    - µ2
    		1.40.36660569677.106290.680179382.1198206


    What can you conclude about the difference in weights between one-year-old boys and girls based on this interval?












    There is no significant difference in the weights of one-year-old boys and girls.
    There is a significant difference in the weights of one-year old boys and girls. We are 95% confident that boys weigh from 0.68lbs to 2.12 lbs more than girls at this age.
    There is a significant difference in the weights of one-year old boys and girls. We are 95% confident that girls weigh from 0.68lbs to 2.12 lbs more than boys at this age.

    2 points


    Question 7


  13. A group of five individuals with high blood pressure were given a new drug that was designed to lower blood pressure. Systolic blood pressure was measured before and after treatment for each individual. The results follow.





























  14. Individual12345
    Before170164168158183
    After145132129135145


    STATCRUNCH produced the following results for a 95% confidence interval for the mean reduction in systolic blood pressure.

    Paired T confidence interval:

    µD
    = µ1
    - µ2
    : Mean of the difference between After and Before

    95% confidence interval results:






















    Difference

    Mean

    Std. Err.

    DF

    L. Limit

    U. Limit
    After - Before-31.43.26496554-40.464997-22.335003

    A pharmaceutical representative claims the new drug reduces mean systolic blood pressure by more than 25 points. Does the confidence interval support this claim?









    The confidence interval supports this claim.
    The confidence interval does not support this claim.


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May 08, 2022
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