Question

full (but brief) write-up that must include:

• introduction/context for the problem
• statement of hypotheses (in words as well as symbols)
• checking of assumptions for test (should include histogram, boxplot, interpretations, decision
• calc'n of P-value with proper notation (with explanation)
• decision for test (with context/explanation)
• estimate, if needed.

Freshman IQ	Senior IQ
98	108
104	111
126	136
74	81
86	88
92	95
98	103
110	118
118	120
97	100
83	88
124	138
133	138
101	114
112	114
96	98
89	97
95	104
87	97
93	102

Answer 1

Introduction / Context for the problem

We are given the Freshman I.Q and Senior I.Q. We have to test whether the two I.Q.'s diifer significantly as regards their effect or may be these both I.Q are of different age groups and we have to test whether they are having similar I.Q. or different.

Statement of hypothesis

Null Hypothesis (H0) :  There is no significant difference between the mean I.Q. of Freshman and Senior.

H0 =

Alternate Hypothesis (H1) : There is a significant difference between the mean I.Q. of Freshman and Senior.

H1 =

Assumption for Paired t-test

1) When sample sizes are equal.

2) The two samples are not independent but the sample observations are paired together.

we can clearly see from the boxplots that there are more outliers in the Freshman i.q as compared to the Senior I.Q. therefore the data is more skewed and distributed in case of former and can lead the errors in calculations whereas in case od latter the data is having no outliers so this is good data and can be used for further calculations and can give accurate result.

In case of histogram , the former is having mix type of data wheras in case of latter the I.Q. is dropping, so we can infer that as age increases I.Q. starts dropping due to various factors.

DECISION FOR TEST

level of significanvce is 5% (0.05)

p value is 5.124

t calculated is 7.5918

t tab is 2.1009

We can infer that as t calculated is greater than t tabulated, therefore we reject the null hypothesis and concludes that there is a significant difference between the mean I.Q. of Freshman and Senior.

now when we compare the p-value and level of significance we can infere the same results as above.

We were unable to transcribe this image

We were unable to transcribe this image

1 E F G HT L M N O P R S 1 Freshman I.Q. Senior I.Q 98 108 FRESHMAN I.Q. SENIOR I.Q. 104 126 110 118 97 124 133 96 104 97 102

FRESHMAN I.Q. SENIOR I.Q. [74,94] (94, 114] (114, 134] [81, 102] (102, 123] (123, 144]

1 t-Test: Paired Two Sample for Means 2 3 98 108 100.9473684 251.497076 19 0.975349007 107.4736842 282.4853801 19 4 Mean 5 Variance 6 Observations 7 Pearson Correlation 8 Hypothesized Mean Difference 9 df 10 t Stat 11 P(T<=t) one-tail 12 t Critical one-tail 13 P(T<=t) two-tail 14 t Critical two-tail 15 16 -7.591836735 2.56212E-07 1.734063607 5.12424E-07 2.10092204

The equation used is the test statistic for paired t-test