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

A large sample of size $n = 50$ has mean $\bar{x} = 102$ and standard deviation $s = 6$. Calculate the $t$-statistic for the null hypothesis $H_0: \mu = 100$.

Trials conducted on crop yield ($\text{tonnes ha}^{-1}$) result in $n=11$, $\bar{x}=5.5$ and $s=0.6$. Calculate the value of the $t$-statistic for the null hypothesis $H_0: \mu=5$.

In a manufacturing process, a sample of $n=5$ items has a mean defect count of $\bar{x} = 3.2$ and a sample standard deviation of $s=0.7$.

Calculate the $t$-test statistic for the null hypothesis $H_0: \mu = 2.5$.

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

In a study of blood pressure, $n = 30$ patients have a mean systolic blood pressure of $130\text{ mmHg}$ and a sample standard deviation of $s = 12\text{ mmHg}$. Calculate the value of the $t$-test statistic for the null hypothesis $H_0: \mu = 135\text{ mmHg}$.

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 study of cholesterol levels, measured in $\text{mg/dL}$, was conducted with a sample of $n = 40$ subjects. The sample mean was found to be $\bar{x} = 190$ and the sample standard deviation was $s = 30$.

Calculate the $t$-test statistic for the null hypothesis $H_0: \mu = 200$.

The reaction times (in seconds) of $n = 9$ drivers have a sample mean of $\bar{x} = 12.5$ and a sample standard deviation of $s = 2.3$.

Calculate the $t$-statistic for testing the null hypothesis $H_0 : \mu = 15$.

Customer satisfaction scores ($1$–$5$) for $n=20$ individuals have a mean of $\bar{x} = 4.2$ and a standard deviation $s = 0.5$. Calculate the $t$-statistic for the null hypothesis $H_0: \mu = 4$.

In a water quality test, a sample of $n = 6$ pH readings has an average of $7.3$ with a sample standard deviation of $s = 0.05$.

Calculate the $t$-test statistic for the null hypothesis $H_0: \mu = 7.4$.

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

The reaction times, in seconds, of $n = 14$ subjects were recorded. The sample mean was $\bar{x} = 0.62$ and the sample standard deviation was $s = 0.08$.

Calculate the value of the $t$-test statistic to test the null hypothesis $H_0: \mu = 0.65$.

A manufacturer tests 15 bolts and finds an average breaking force of $120\text{ N}$ with a standard deviation of $8\text{ N}$. Calculate the value of the $t$-statistic to test the null hypothesis $H_0: \mu = 115\text{ N}$.

Baggage weights from a sample of $n = 18$ flights have a mean weight of $\bar{x} = 24.7\text{ kg}$ and a standard deviation of $s = 2.1\text{ kg}$.

Find the value of the $t$-statistic for the hypothesis test $H_0: \mu = 23$.

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

A small lab counts $n = 8$ bacterial colonies and finds a sample mean $\bar{x} = 22$ and a sample standard deviation $s = 3$.

Calculate the $t$-statistic for the null hypothesis $H_0: \mu = 20$.