Final answer:
The turning point test of randomness is used to assess whether a series of data is random by comparing the number of observed turning points with the expected number under a normal distribution approximation when the sample size is large.
Step-by-step explanation:
The turning point test of randomness, also known as the nonparametric test, is a method used to determine whether a series of data points is random. This test is based on the number of turning points (where the direction of the trend changes) within the series. When applying this test to the given process Yt = 0.1Zt - 0.7Zt-1, where {Zt} represents white noise innovations, you are to compare the observed number of turning points to the expected number in a random series.
When the number of observations 'n' is large, the number of turning points 'P' in a random series can be approximated by a normal distribution with mean 2(n - 2)/3 and variance (16n - 29) / 90. With 70 observations for sweet-potato yield, you would first calculate the expected mean and variance of 'P', then count the number of observed turning points in your data, and finally assess whether the observed number of turning points is significantly different from the expected number under the assumption of randomness. Any significant deviation might suggest non-randomness in the data.