• Our study was established to answer several questions. Is there a relationship between the amount of texts a person sends and the grade the person is in? Furthermore, is there a correlation between the amount of texts males send and the amount of texts females send?
    • We obtained our samples by using stratified random samples. We input all the names of students in North Olmsted High School into Minitab and split them into different groups based on their grade and gender. After they were appropriately split, we used a random generator on Minitab to select 40 people from each different group. The total sample included 320 people. The population of interest was the students of North Olmsted High School. Because our study required a sample for the amount of texts individuals sent as of last month, we did use a survey.
    • Survey:
    • What is your age?
    • What is your grade level?
    • What is your gender?
    • Do you text?   Y     N
    • If so, how much sent/received last month?

Graphs

Data

Chi-Square Analysis for grade level

Ho: There is no association between grade level and number of texts a person sends.

Ha: There is an association between grade level and number of texts a person sends.

α = 0.05

Tabulated statistics: grade, Category 

Rows: grade   Columns: Category

           1      2      3      4      5     6     All

9         19     12     12      9     15     3      70
       17.12  12.02   9.91  15.92  13.22  1.80   70.00

10        18      8      5     18     13     1      63
       15.41  10.82   8.92  14.33  11.90  1.62   63.00

11        11     11      6     17     13     1      59
       14.43  10.13   8.36  13.42  11.14  1.52   59.00

12         9      9     10      9      3     1      41
       10.03   7.04   5.81   9.33   7.74  1.06   41.00

All       57     40     33     53     44     6     233
       57.00  40.00  33.00  53.00  44.00  6.00  233.00

Cell Contents:      Count
                    Expected count

Pearson Chi-Square = 18.460, DF = 15, P-Value = 0.239
Likelihood Ratio Chi-Square = 19.577, DF = 15, P-Value = 0.189

Conclusion: Because the p-value is greater than alpha, we fail to reject the null hypothesis at the 0.05 level of significance. Thus, there is insufficient evidence that there is a relationship between the grade level of a student and the amount of texts the person sends.

 

Chi-Square Analysis for Gender

Ho: There is no association between grade level and number of texts a person sends.

Ha: There is an association between grade level and number of texts a person sends.

α = 0.05

Tabulated statistics: gender, Category 

Rows: gender   Columns: Category

           1      2      3      4      5     6     All

F         27     16     21     22     23     3     112
       27.40  19.23  15.86  25.48  21.15  2.88  112.00

M         30     24     12     31     21     3     121
       29.60  20.77  17.14  27.52  22.85  3.12  121.00

All       57     40     33     53     44     6     233
       57.00  40.00  33.00  53.00  44.00  6.00  233.00

Cell Contents:      Count
                    Expected count

Pearson Chi-Square = 5.492, DF = 5, P-Value = 0.359
Likelihood Ratio Chi-Square = 5.534, DF = 5, P-Value = 0.354

Conclusion: Because the p-value is greater than alpha, we fail to reject the null hypothesis at the 0.05 level of significance. Thus, there is insufficient evidence that there is a relationship between gender and the amount of texts a person sends.

 

Two-Sample T-Test for Average Mean Texts between Freshman and Seniors

Ho: The mean average texts freshman and seniors send are the same.

 Ha: The mean average texts freshman send is greater than the amount seniors send.

α = 0.05

Because the sample of freshman was 70 and the sample of seniors was 41, the Central Limit Theorem applies and the distributions can be assumed to be normal. Both samples are a random sample of their respective grades. Since the two samples are from separate grades, they have to be independent.

Two-Sample T-Test and CI: average texts, grade 

Two-sample T for average texts

grade   N  Mean  StDev  SE Mean
 9     70  4961   9780     1169
12     41  2295   5491      858

Difference = mu ( 9) - mu (12)
Estimate for difference:  2666
95% lower bound for difference:  261
T-Test of difference = 0 (vs >): T-Value = 1.84  P-Value = 0.034  DF = 108

Conclusion: Because the P-value is less than alpha, we reject the null hypothesis at the 0.05 level of significance. Thus, there is sufficient evidence that the amount of texts freshman send on average is greater than the amount of texts seniors send on average.