Paper 1 · November 2018 · Hypothesis Testing

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?

Model answer

-1.82

Also accepted: -1.819

Explanation

Sample mean = 79.53/80 = 0.9941. Unbiased variance s^2 = [sum(x^2) - n(mean)^2]/(n-1) = [100.4621 - 80(0.9941)^2]/79 = 0.2709, so s = 0.5205. t = (0.9941-1.10)/(0.5205/sqrt(80)) = -0.1059/0.0582 = -1.82.

Derived from ZIMSEC Statistics Paper 1, November 2018, Q9

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A random sample of 80 pockets of manure gives ∑x=79.53\sum x=79.53∑x=79.53 and ∑x2=100.4621\sum x^2=100.4621∑x2=100.4621 (in kg). Testing H0:μ=1.10H_0:\mu=1.10H0​:μ=1.10 against H1:μ<1.10H_1:\mu<1.10H1​:μ<1.10, what is the value of the test statistic ttt, to 2 decimal places?

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Get the full paper, not just one question

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?