Question

Practice for Hypothesis Testing (with z)

5. A farmer has found over the years that the average height of a corn plant is 77.4 inches with a standard deviation of 7.3 inches. A seed company promises that their seeds produce taller plants. The farmer plants 45 of their seeds and the resulting plants had a mean height of 80.3 inches. Test the seed company’s claim using a= .025 and the prob-value approach.

Answer 1

Let $\mu$ denotes the average height of a corn plant from the seed that the company produced.

To test null hypothesis Ho :f = 77.4 against alternative hypothesis H1 :4 > 77.4 Let i denotes the sample mean, o denotes the sample standard deviation and n denotes the sample size. Here, ī = 80.300,02 = 53.2900,0 = 7.30, n = 45 The test statistic can be written as: 2= Vnce – 77.4) which under H, follows a standard normal distribution. We reject Ho at 0.025 level of significance if P-value < 0.025 or if Zobs > 20.025 Now, The value of the test statistic = 2.664903 The critical value = 1.959964 P – value = P(Z > 2.664903) = 1 - P(Z < 2.664903) = 1 – 0.996149 = 0.003851 Since p-value < 0.025 and Zobs > Zcritical = 1.959964, so we reject Ho at 0.025 level of significance Hence, we can conclude that population mean is significantly greater than 77.4

Conclusion : There is sufficient evidence to support the company's claim as the average height of a corn plant from the seed that the company produced is significantly greater than 77.4 inches.