IB Mathematics Applications & Interpretation Question Type 13: Determining the Type of Two Sample T-test and Calculating the According T-statistic Exercises

Reaction times of 10 subjects are measured before and after training. The mean difference (after $-$ before) is $-0.12\text{ s}$ with $s_d=0.05\text{ s}$. State the type of test to be used and calculate the value of the $t$-statistic.

Identify the $t$-test type and compute the $t$-statistic for two independent samples with unequal variances: $n_1=15$, $n_2=12$, ${\bar{x}}_1=78.5$, ${\bar{x}}_2=74.2$, $s_1=8.4$, $s_2=9.1$.

Blood pressure is measured on 16 patients at two visits. The mean difference (visit 2 $-$ visit 1) is $-6\text{ mmHg}$ with $s_d=8$. Identify the test and compute the $t$-statistic.

The lifespans of two battery types are tested independently with the following results: $n_1=20$, $n_2=22$, ${\bar{x}}_1=1200\text{ h}$, ${\bar{x}}_2=1150\text{ h}$, $s_1=100$, $s_2=150$.

Identify the appropriate t-test for these samples and compute the value of the $t$-statistic.

A study measures the same 8 subjects before and after a treatment. The mean difference (after $-$ before) is $2.5$ units with a sample standard deviation of differences $s_d=1.2$.

Identify the $t$-test used and calculate the $t$-statistic.

A drug trial measures cholesterol in $12$ patients before and after treatment. The mean difference (before$-$after) is $5\text{ mg/dL}$ with $s_d=3.5$. Identify the test and find the $t$-statistic.

For two independent samples from normally distributed populations with equal variances, the following summary statistics were calculated:

Sample 1: $n_1=25$, ${\bar{x}}_1=170$, $s_1=6$ Sample 2: $n_2=30$, ${\bar{x}}_2=165$, $s_2=5.5$

Calculate the value of the $t$-statistic for a two-sample $t$-test.

Determine the type of $t$-test to be used and calculate the $t$-statistic for independent samples, assuming equal variances, given the following data: $n_1=18$, $n_2=18$, ${\bar{x}}_1=82$, ${\bar{x}}_2=78$, $s_1=7$, $s_2=7$.

Determine the appropriate $t$-test type and calculate the $t$-statistic for two independent samples assuming equal variances with $n_1=10$, $n_2=12$, ${\bar{x}}_1=5.2$, ${\bar{x}}_2=4.7$, $s_1=1.1$, $s_2=1.3$.

Identify the $t$-test and compute the $t$-statistic for two independent samples with unequal variances: $n_1=8,n_2=10,{\bar{x}}_1=50.5,{\bar{x}}_2=47.2,s_1=2.5,s_2=3.1$.

Identify the t-test and compute the t-statistic for two independent samples with unequal variances: $n_1=14$, $n_2=14$, ${\bar{x}}_1=200$, ${\bar{x}}_2=190$, $s_1=15$, $s_2=20$.

Determine the t-test type and calculate the t-statistic for independent samples assuming equal variances: $n_1=20$, $n_2=22$, ${\bar{x}}_1=15.3$, ${\bar{x}}_2=13.8$, $s_1=4.2$, $s_2=3.9$.