Question

For the study described below identify a statistical test that can be used to solve the problem or questions. Be sure to specify the appropriate hypotheses or formula and associated assumptions.

In Virginia, when the temperature falls to 30⁰F, the probability that a citrus tree will show measurable damage is 0.10. A group of farmers think that the probability is much higher than 0.10. To test this they use a small orchard with 32 citrus trees as their sample.

Answer 1

Solution:-

We will use one sample z test for proportion.

The appropriate hypotheses or formula are:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: P < 0.10
Alternative hypothesis: P > 0.10

The associated assumptions are:-

1) The sampling method is simple random sampling.

2) Each sample point can result in just two possible outcomes.

3) The sample includes at least 10 successes and 10 failures.

4) The population size is at least 20 times as big as the sample size.