Problem

An agricultural researcher is interested in estimating the mean length of the growing season in a region. Treating the last 10 years as a simple random sample, he obtains the following data, which represent the number of days of the growing season. What is the point estimate of the population mean number of days of the growing season? 153 158 143 145 166 185 186 180 169 147 The point estimate is $\square$ (Type an integer or a decimal. Do not round.)

Solution

Step 1 :An agricultural researcher is interested in estimating the mean length of the growing season in a region. Treating the last 10 years as a simple random sample, he obtains the following data, which represent the number of days of the growing season: 153, 158, 143, 145, 166, 185, 186, 180, 169, 147.

Step 2 :To find the point estimate of the population mean number of days of the growing season, we need to calculate the sample mean. The sample mean is the sum of all the values divided by the number of values.

Step 3 :Let's calculate the sum of the number of days: \(153 + 158 + 143 + 145 + 166 + 185 + 186 + 180 + 169 + 147 = 1632\).

Step 4 :There are 10 values in the sample, so the sample mean is \( \frac{1632}{10} = 163.2 \).

Step 5 :So, the point estimate of the population mean number of days of the growing season is \(\boxed{163.2}\).

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