Hypothesis Testing Questions and Answers

A random sample of 80 pockets of manure gives $\sum x=79.53$ and $\sum x^2=100.4621$ (in kg). Testing $H_0:\mu=1.10$ against $H_1:\mu<1.10$, what is the value of the test statistic $t$, to 2 decimal places?

A test of $H_0:\mu=1.10$ kg against $H_1:\mu<1.10$ kg for the mass of manure pockets gives a test statistic of $t=-1.82$ with 79 degrees of freedom, compared against a one-tailed 5% critical value of $-1.664$. What is the correct conclusion?

Which statement correctly distinguishes a statistic from a parameter?

A sample of 10 toothpick lengths (cm): 4.99, 4.96, 5.00, 4.98, 5.01, 4.95, 4.96, 4.97, 4.99, 4.97 gives a sample mean of 4.978 cm and standard deviation of about 0.107 cm. Testing H0: mu = 5 against H1: mu is not equal to 5 at the 1% significance level gives a t-statistic of about -0.649, compared with a critical value of t(9) = 3.250. What is the conclusion?

A driver records the times (minutes) taken to complete a 50 km lap over 30 laps: Time 23 (frequency 3), 24 (7), 25 (8), 26 (6), 27 (3), 28 (2), 29 (1). What is the sample mean lap time, to 1 decimal place?

A sample of 30 lap times has mean 25.3 minutes and standard deviation 1.218 minutes. Testing $H_0:\mu=25$ against $H_1:\mu>25$, what is the value of the test statistic?