IGNOU MST 4 2018 - Results of a survey by the National Centre for Health Statistics indic

Question

Results of a survey by the National Centre for Health Statistics indicated that people between 65 and 74 years of age contact a physician an average of 9.8 times per year. People 75 and older contact physicians an average of 12.9 times per year. Suppose you want to validate these results by taking your own samples and obtained the following data represent the number of annual contacts people make with a physician. The samples are independent.

Number of annual contacts people make

with a physician

65 to 74

75 and Older

i) Formulate the hypotheses that average number of contacts with physician by people

75 and older is greater than the number by people 65 to 74 years old.

ii) What assumptions are necessary to apply the t-test.

iii) Apply the t-test for testing the hypotheses formulated in (i) using α = 0.05.

iv) If assumptions in (ii) are not fulfilled, then which test is applied in this situation and why?

v) Apply the test for (iv) and compare the result with (iii).

16 Feb 2018

Answer :

Word Count : 992

Let's solve this step by step manually. We are comparing the mean number of annual physician contacts between two independent age groups: 65–74 and 75+. --- ## Step (i): Formulate Hypotheses Let: $$ \mu_1 = \text{mean for 65–74 years old}, \quad \mu_2 = \text{mean for 75+ years old} $$ We want to test if the older group has a higher mean: $$ H_0: \mu_2 \le \mu_1 \quad (\text{no difference or less}) $$ $$ H_1: \mu_2 > \mu_1 \quad (\text{older people contact more}) $$ This is a one-tailed test. --- ## Step (ii): Assumptions for t-test 1. Independence: The two samples are independent. ✅ 2. Normality: The distribution of contacts is approximately normal in both populations. 3. Equal variances (optional): If using pooled t-test, we assume equal variances; otherwise, use Welch’s t-test for unequal variances. --- ## Step (iii): Apply t-test ### Step 1: Organize the data 65–74: 12, 13, 8, 11, 9, 6, 11 → $n_1 = 7$ 75+: 16, 15, 10, 17, 13, 12, 14, 9, 13 → $n_2 = 9$ --- ### Step 2: Compute sample means $$ \bar{x}_1 = \frac{12 + 13 + 8 + 11 + 9 + 6 + 11}{7} = \frac{70}{7} = 10 $$ $$ \bar{x}_2 = \frac{16 + 15 + 10 + 17 + 13 + 12 + 14 + 9 + 13}{9} $$ Sum step-by-step: 16 + 15 = 31 31 + 10 = 41 41 + 17 = 58 58 + 13 = 71 71 + 12 = 83 83 + 14 = 97 97 + 9 = 106 106 + 13 = 119 $$ \bar{x}_2 = \frac{119}{9} \approx 13.22 $$ --- ### Step 3: Compute sample standard deviations

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IGNOU Solved Assignments Assignments Ignou Projects Project Previous Year Solved Exam Papers Notes Notes Sample Question Papers Sample Question Papers

Educational attainment	Income Categories			Total
Educational attainment	Low	Middle	High	Total
No college UG PG Doctoral	32 13 43 12	20 16 51 13	23 1 60 15	75 30 154 41
Total	100	100	100	300

S. No.	Breaking Pressure
S. No.	Iron	Copper
1	72.7	73
2	69.6	67.2
3	83.4	75.3
4	78.9	61.4
5	75	74
6	71.6	69.5
7	85.7	69.8
8	73.5	73.8
9	70.4	68
10	84.2	76.1

S. No.	Test For	Name of the Test	Test Statistic	Assumptions for Applying the Test	Test Type
1	Population mean when population variance is known and population is normal	Z-test	$Z= \frac{X - \mu }{\sigma /\sqrt{n}}$	1. Sample observations should be independent. 2. The measurement scale should be at least interval scale.	Parametric Test
2	Population mean when population variance is unknown and population is normal
3	Population mean/median when the form of population is not known and sample size is small
4	Population mean/median when the form of population is not known and the data is in ordinal scale and sample