1.
Continuous variables in the data
- Age in years.
- A number of medications used.
Categorical variables in the data
- Participant ID Number.
- Preferred Language.
- It fractured hip, leg, arm or spine.
- Ability to take care of own personal needs.
- Past smoke history.
2.
Frequencies and Percentages for the Categorical variables
| Preferred Language | |||||
| Frequency | Percent | Valid Percent | Cumulative Percent | ||
| Valid | English | 29 | 43.9 | 43.9 | 43.9 |
| Spanish | 37 | 56.1 | 56.1 | 100.0 | |
| Total | 66 | 100.0 | 100.0 | ||
| Fractured hip, leg, arm or spine | |||||
| Frequency | Percent | Valid Percent | Cumulative Percent | ||
| Valid | No | 55 | 83.3 | 83.3 | 83.3 |
| Yes | 11 | 16.7 | 16.7 | 100.0 | |
| Total | 66 | 100.0 | 100.0 | ||
| Ability to care of own personal needs | |||||
| Frequency | Percent | Valid Percent | Cumulative Percent | ||
| Valid | Can do | 38 | 57.6 | 57.6 | 57.6 |
| Can do with some difficulty | 15 | 22.7 | 22.7 | 80.3 | |
| Cannot do without help | 13 | 19.7 | 19.7 | 100.0 | |
| Total | 66 | 100.0 | 100.0 | ||
| Smoke status | |||||
| Frequency | Percent | Valid Percent | Cumulative Percent | ||
| Valid | Nonsmoker | 42 | 63.6 | 63.6 | 63.6 |
| smoker | 24 | 36.4 | 36.4 | 100.0 | |
| Total | 66 | 100.0 | 100.0 | ||
| Participant ID Number | |||||
| Frequency | Percent | Valid Percent | Cumulative Percent | ||
| Valid | AA-31 | 1 | 1.5 | 1.5 | 1.5 |
| AD-29 | 1 | 1.5 | 1.5 | 3.0 | |
| AF-02 | 1 | 1.5 | 1.5 | 4.5 | |
| AG-25 | 1 | 1.5 | 1.5 | 6.1 | |
| AG-45 | 1 | 1.5 | 1.5 | 7.6 | |
| AM-01 | 1 | 1.5 | 1.5 | 9.1 | |
| BS-52 | 1 | 1.5 | 1.5 | 10.6 | |
| CC-63 | 1 | 1.5 | 1.5 | 12.1 | |
| CK-42 | 1 | 1.5 | 1.5 | 13.6 | |
| CN-18 | 1 | 1.5 | 1.5 | 15.2 | |
| CR-03 | 1 | 1.5 | 1.5 | 16.7 | |
| DC-09 | 1 | 1.5 | 1.5 | 18.2 | |
| DH-33 | 1 | 1.5 | 1.5 | 19.7 | |
| EG-24 | 1 | 1.5 | 1.5 | 21.2 | |
| EG-46 | 1 | 1.5 | 1.5 | 22.7 | |
| EK-34 | 1 | 1.5 | 1.5 | 24.2 | |
| EM-51 | 1 | 1.5 | 1.5 | 25.8 | |
| FA-50 | 1 | 1.5 | 1.5 | 27.3 | |
| FP-04 | 1 | 1.5 | 1.5 | 28.8 | |
| GC-05 | 1 | 1.5 | 1.5 | 30.3 | |
| GK-11 | 1 | 1.5 | 1.5 | 31.8 | |
| GV-23 | 1 | 1.5 | 1.5 | 33.3 | |
| HC-10 | 1 | 1.5 | 1.5 | 34.8 | |
| HK-12 | 1 | 1.5 | 1.5 | 36.4 | |
| HL-17 | 1 | 1.5 | 1.5 | 37.9 | |
| HL-55 | 1 | 1.5 | 1.5 | 39.4 | |
| IH-54 | 1 | 1.5 | 1.5 | 40.9 | |
| JB-47 | 1 | 1.5 | 1.5 | 42.4 | |
| JC-22 | 1 | 1.5 | 1.5 | 43.9 | |
| JC-39 | 1 | 1.5 | 1.5 | 45.5 | |
| JJ-49 | 1 | 1.5 | 1.5 | 47.0 | |
| JK-13 | 1 | 1.5 | 1.5 | 48.5 | |
| JK-36 | 1 | 1.5 | 1.5 | 50.0 | |
| JMC-56 | 1 | 1.5 | 1.5 | 51.5 | |
| KC-59 | 1 | 1.5 | 1.5 | 53.0 | |
| KK-14 | 1 | 1.5 | 1.5 | 54.5 | |
| KK-35 | 1 | 1.5 | 1.5 | 56.1 | |
| KL-57 | 1 | 1.5 | 1.5 | 57.6 | |
| KP-64 | 1 | 1.5 | 1.5 | 59.1 | |
| KS-20 | 1 | 1.5 | 1.5 | 60.6 | |
| LC-06 | 1 | 1.5 | 1.5 | 62.1 | |
| MG-30 | 1 | 1.5 | 1.5 | 63.6 | |
| ML-41 | 1 | 1.5 | 1.5 | 65.2 | |
| MP-48 | 1 | 1.5 | 1.5 | 66.7 | |
| MR-32 | 1 | 1.5 | 1.5 | 68.2 | |
| MW-67 | 1 | 1.5 | 1.5 | 69.7 | |
| OY-65 | 1 | 1.5 | 1.5 | 71.2 | |
| RG-07 | 1 | 1.5 | 1.5 | 72.7 | |
| RG-26 | 1 | 1.5 | 1.5 | 74.2 | |
| RO-53 | 1 | 1.5 | 1.5 | 75.8 | |
| RP-28 | 1 | 1.5 | 1.5 | 77.3 | |
| RR-27 | 1 | 1.5 | 1.5 | 78.8 | |
| SHC-58 | 1 | 1.5 | 1.5 | 80.3 | |
| SIC-62 | 1 | 1.5 | 1.5 | 81.8 | |
| SJ-08 | 1 | 1.5 | 1.5 | 83.3 | |
| SJ-43 | 1 | 1.5 | 1.5 | 84.8 | |
| SK-15 | 1 | 1.5 | 1.5 | 86.4 | |
| SKC-61 | 1 | 1.5 | 1.5 | 87.9 | |
| SWK-66 | 1 | 1.5 | 1.5 | 89.4 | |
| TP-19 | 1 | 1.5 | 1.5 | 90.9 | |
| WC-40 | 1 | 1.5 | 1.5 | 92.4 | |
| YJK-37 | 1 | 1.5 | 1.5 | 93.9 | |
| YK-16 | 1 | 1.5 | 1.5 | 95.5 | |
| YK-60 | 1 | 1.5 | 1.5 | 97.0 | |
| YL-68 | 1 | 1.5 | 1.5 | 98.5 | |
| YYK-38 | 1 | 1.5 | 1.5 | 100.0 | |
| Total | 66 | 100.0 | 100.0 | ||
Means and Standard deviations for the Continuous variables
| Statistics | |||
| Age in Years | Number of Medications used regularly | ||
| N | Valid | 66 | 66 |
| Missing | 0 | 0 | |
| Mean | 74.73 | 3.27 | |
| Median | 73.50 | 3.00 | |
| Mode | 71 | 0 | |
| Std. Deviation | 6.365 | 3.554 | |
| Variance | 40.509 | 12.632 | |
| Skewness | .341 | 1.658 | |
| Std. Error of Skewness | .295 | .295 | |
| Range | 26 | 18 | |
| Minimum | 63 | 0 | |
| Maximum | 89 | 18 | |
| Sum | 4932 | 216 | |
Question 3;
Null Hypothesis: The Proportion of English speaking patients is greater than 50%
Alternative Hypothesis: The Proportion of English speaking patients is not greater than 50%
Total number of patients = 66
Number of English speaking patients = 29
Proportion of English speaking patients = (29/66)
= 0.4393
= 43.93%
- Standard error and Z statistic
Let p be the proportion of English Speaking patients and the N be the total number of patients. The standard error was calculated using the following formula;
Standard Error =
Standard Error =
- Critical Z Value and the P value
The critical Z value from the tables is 1.6449 at alpha = 0.05
The P value was calculated using the following Excel code:
NORM.DIST (0.4393, 50, 0.061092, 1) and was found to be 0.000
The p value is less than Alpha = 0.05 hence the p value is significant. We reject the Null hypothesis and conclude that the proportion of English speaking patients is not greater than 50%.
There is no enough evidence to support the null hypothesis.
Question 4;
a)
Hypothesis for the t-test
Null hypothesis: The Population mean for Nonsmoker group is equal to population mean of Smoker group
Alternative hypothesis: The Population mean for Nonsmoker group is not equal to population mean of Smoker group
Hypothesis for levene’s test
Null hypothesis: The population variances of group1 and group2 are equal
Alternative hypothesis: The population variances of group1 and group2 are not equal
b)
| Group Statistics | |||||
| Smoke status | N | Mean | Std. Deviation | Std. Error Mean | |
| Number of Medications used regularly | Nonsmoker | 42 | 2.98 | 3.127 | .483 |
| smoker | 24 | 3.79 | 4.222 | .862 | |
| Independent Samples Test | ||||||||||
| Levene’s Test for Equality of Variances | t-test for Equality of Means | |||||||||
| F | Sig. | t | df | Sig. (2-tailed) | Mean Difference | Std. Error Difference | 95% Confidence Interval of the Difference | |||
| Lower | Upper | |||||||||
| Number of Medications used regularly | Equal variances assumed | .755 | .388 | -.895 | 64 | .374 | -.815 | .911 | -2.635 | 1.004 |
| Equal variances not assumed | -.826 | 37.610 | .414 | -.815 | .988 | -2.816 | 1.185 | |||
The calculated mean for smoker group is 2.98 while the calculated mean for non-smoker group is 3.79
c)
Confidence interval when equal variances are assumed
[-2.635, 1.004]
Lower limit = -2.635 Upper limit = 1.004
Confidence interval when equal variances are not assumed
[-2.816, 1.185]
Lower limit = -2.816 Upper limit = 1.185
d)
When equal variances are assumed, the critical t value is -0.895
When equal variances are not assumed the critical t value is -0.826
e)
The p value is 0.388. The p value is greater than 0.01. (0.388>0.01)
We therefore fail to reject the null hypothesis and conclude that the means for the Nonsmoker group and the Smoker group are not significantly different.