Question Type 10: Calculating the t-statistics for one sample t-tests Exercises

A sample of 10 observations has a sample mean of $5.2$, a sample standard deviation of $0.5$, and you wish to test $H_0:\ \\mu=5$. Calculate the $t$-statistic for this one-sample $t$-test.

In a sample of 20 student scores, the mean score is $78$ with $s=10$. Calculate the $t$-statistic to test $H_0:\mu=75$.

A health study measures weights ($\mathrm{kg}$) for $n=25$ individuals: $\bar x=70$, $s=4.5$. Find the $t$-statistic to test $H_0:\mu=68$.

A manufacturer tests 15 bolts and finds an average breaking force of $120\,$N with a standard deviation of $8\,$N. Test $H_0:\mu=115\,$N by calculating the $t$-statistic.

A small lab counts $n=8$ bacterial colonies: $\bar x=22$, $s=3$. Calculate the $t$-statistic for $H_0:\mu=20$.

A large sample ($n=50$) has mean $102$ and $s=6$. Compute the $t$-statistic for $H_0:\mu=100$.

In a study of blood pressure, $n=30$ patients have mean systolic BP $130\,$mmHg, $s=12\,$mmHg. Compute $t$ for $H_0:\mu=135\,$mmHg.

Reaction times (s) of $n=9$ drivers have mean $12.5$ and $s=2.3$. Calculate $t$ for testing $H_0:\mu=15$.

A battery life test on 12 units yields a mean of $210$ hours and $s=15$ hours. Compute the $t$-statistic for $H_0:\mu=200$.

In manufacturing, $n=5$ items have mean defect count $3.2$, $s=0.7$. Compute $t$ for $H_0:\mu=2.5$.

Reaction times ($s$) of $n=14$ subjects: $\bar x=0.62$, $s=0.08$. Calculate $t$ to test $H_0:\mu=0.65$.

Baggage weights ($\mathrm{kg}$) from $n=18$ flights average $24.7$ with $s=2.1$. Find $t$ for $H_0:\mu=23$.

Customer satisfaction scores ($1$–$5$) for $n=20$ individuals: mean $4.2$, $s=0.5$. Compute the $t$-statistic for $H_0:\mu=4$.

Cholesterol levels ($\mathrm{mg/dL}$) of $n=40$ subjects: $\bar x=190$, $s=30$. Calculate $t$ for $H_0:\mu=200$.

A water quality test: $n=6$ pH readings average $7.3$ with $s=0.05$. Find $t$ for $H_0:\mu=7.4$.

A trials on crop yield ($\mathrm{tons/ha}$) give $n=11$, $\bar x=5.5$, $s=0.6$. Find $t$ for $H_0:\mu=5$.