Question

ch 20 the time (in number of days) until maturity of a certain variety of tomato plant is normally distributed. i select a simple random sample of four plants of this variety and measure the time until maturity. the sample yields xbar = 65 with standard deviation s = 2.4. you read on the package of seeds that these tomatoes reach maturity, on average, in 61 days. you want to test to see if your seeds are reaching maturity later than expected, which might indicate that your package of seeds is too old. the appropriate hypotheses are
ho: mu = 65, ha: mu ≠ 65,
ho: mu = 65, ha: mu > 65,
ho: mu = 61, ha: mu > 61,
ho: mu = 61, ha: mu ≠ 61.

Explanation:

In hypothesis testing, the null hypothesis \(H_0\) represents the status - quo or the claim that is initially assumed to be true. Here, the claim on the package is that the average time until maturity is \(\mu = 61\) days, so \(H_0:\mu=61\). The alternative hypothesis \(H_a\) is what we are trying to find evidence for. Since we want to test if the seeds are reaching maturity later (i.e., the average time is greater than the claimed average), \(H_a:\mu > 61\).

Answer:

\(H_0:\mu = 61,H_a:\mu>61\)