Question

In: Statistics and Probability

Is there a difference between community college statistics students and university statistics students in what technology...

Is there a difference between community college statistics students and university statistics students in what technology they use on their homework? Of the randomly selected community college students 67 used a computer, 86 used a calculator with built in statistics functions, and 22 used a table from the textbook. Of the randomly selected university students 40 used a computer, 88 used a calculator with built in statistics functions, and 39 used a table from the textbook. Conduct the appropriate hypothesis test using an αα = 0.01 level of significance.

  1. What is the correct statistical test to use?
    • Goodness-of-Fit
    • Independence
    • Homogeneity
    • Paired t-test
  2. What are the null and alternative hypotheses?
    H0:H0:
    • Type of student and type of technology used for statistics homework are dependent.
    • Type of student and type of technology used for statistics homework are independent.
    • The distribution of the technology that community college statistics students use for their homework is the same as the distribution of the technology that university statistics students use for their homework.
    • The distribution of the technology that community college statistics students use for their homework is not the same as the distribution of the technology that university statistics students use for their homework.



    H1:H1:
    • The distribution of the technology that community college statistics students use for their homework is the same as the distribution of the technology that university statistics students use for their homework.
    • Type of student and type of technology used for statistics homework are independent.
    • The distribution of the technology that community college statistics students use for their homework is not the same as the distribution of the technology that university statistics students use for their homework.
    • Type of student and type of technology used for statistics homework are dependent.
  3. The test-statistic for this data =  (Please show your answer to 2 decimal places.)
  4. The p-value for this sample = (Please show your answer to 4 decimal places.)
  5. The p-value is Select an answer less than (or equal to) greater than  αα
  6. Based on this, we should
    • accept the null
    • fail to reject the null
    • reject the null
  7. Thus, the final conclusion is...
    • There is sufficient evidence to conclude that the distribution of the technology that community college statistics students use for their homework is the same as the distribution of the technology that university statistics students use for their homework.
    • There is insufficient evidence to conclude that type of student and type of technology used for statistics homework are independent.
    • There is sufficient evidence to conclude that type of student and type of technology used for statistics homework are dependent.
    • There is insufficient evidence to conclude that the distribution of the technology that community college statistics students use for their homework is not the same as the distribution of the technology that university statistics students use for their homework.
    • There is sufficient evidence to conclude that the distribution of the technology that community college statistics students use for their homework is not the same as the distribution of the technology that university statistics students use for their homework.

Solutions

Expert Solution

Number of variables = 1 ( Technology they use on their homework)

Number of samples = 2 (community college statistics students and university statistics students )

We chi-square test of homogeneity for a single categorical variable from two or more different populations.

Homogeneity

H0: The distribution of the technology that community college statistics students use for their homework is the same as the distribution of the technology that university statistics students use for their homework.

H1: The distribution of the technology that community college statistics students use for their homework is not the same as the distribution of the technology that university statistics students use for their homework.

Observed frequencies are,

computer calculator textbook Total
community college students 67 86 22 175
university statistics students 40 88 39 167
Total 107 174 61 342

Expected frequencies are,

computer calculator textbook Total
community college students (175 * 107)/342 = 54.75146 (175 * 174)/342 = 89.03509 (175 * 61)/342 = 31.21345 175
university statistics students (167 * 107)/342 = 52.24854 (167 * 174)/342 = 84.96491 (167 * 61)/342 = 29.78655 167
Total 107 174 61 342

Test statistic,

= 11.39

Degree of freedom, df = (r-1) * (c - 1) = (2 -1) * (3 -1) = 2

P-value = P( > 11.39, df = 2) = 0.0034

The p-value is Select an answer less than α = 0.01

Since p-value is less than the signficance level,

Based on this, we should reject the null

Thus, the final conclusion is...

There is sufficient evidence to conclude that the distribution of the technology that community college statistics students use for their homework is not the same as the distribution of the technology that university statistics students use for their homework.

orchestra answered 1 year ago
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