In a study, researchers wanted to measure the effect of alcohol in the development of the hippocampal region in adolescents. The researchers

Question

In a study, researchers wanted to measure the effect of alcohol in the development of the hippocampal region in adolescents. The researchers randomly selected 30 adolescents with alcohol use disorders to compare the hippocampal volumes in the alcoholic adolescents to the normal volume of 9.08 cubic centimeters. An analysis of the sample data revealed that the hippocampal volume was distributed normally with a mean of 8.25 cm^3 and a standard deviation of 1.67 cm^3.
a. The researchers wanted to determine if the hippocampal values in the alcoholic adolescents were different from the normal volume of 9.08 cm. Write the null and alternative hypotheses for this question. Use a t critical value of 2.045.
b. What are the assumptions (conditions) of this test? Are the assumptions met for this sample?
c. Perform the appropriate test including the formula that you used, the calculated value of the t-statistic, and the t-critical you compared your t-statistic to using a significance level of .05. Then, state your conclusion to the test.
d. Calculate and interpret the 95% confidence interval for the test. Use a t critical of 2.045.

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RuslanHeatt 5 years 2021-09-04T14:59:57+00:00 1 Answers 9 views 0

Answers ( )

  1. phucdien
    0
    2021-09-04T15:01:28+00:00
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    Answer:

    Kindly check explanation

    Step-by-step explanation:

    Given :

    Sample size, n = 30

    Tcritical value = 2.045

    Null hypothesis :

    H0: μ = 9.08

    Alternative hypothesis :

    H1: μ≠ 9.08

    Sample mean, m = 8.25

    Samole standard deviation, s = 1.67

    Test statistic : (m – μ) ÷ s/sqrt(n)

    Test statistic : (8.25 – 9.08) ÷ 1.67/sqrt(30)

    Test statistic : – 0.83 ÷ 0.3048988

    Test statistic : – 2.722

    Tstatistic = – 2.722

    Decision region :

    Reject Null ; if

    Tstatistic < Tcritical

    Tcritical : – 2.045

    -2.722 < – 2.045 ; We reject the Null

    Using the α – level (confidence interval) 0.05

    The Pvalue for the data from Tstatistic calculator:

    df = n – 1 =. 30 – 1 = 29

    Pvalue = 0.0108

    Reject H0 if :

    Pvalue < α

    0.0108 < 0.05 ; Hence, we reject the Null

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