The time, in number of days, until maturity of a certain variety of tomato plant is Normally distributed, with mean μ and standard deviation s = 2.4. You select a simple random sample of four plants of this variety and measure the time until maturity. The sample yields ¯x = 65. 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:

a) H0 : μ = 61 , Hα : μ > 61 .
b) H0 : μ = 65 , Hα : μ < 65 .
c) H0 : μ = 61 , Hα : μ < 61 .
d) H0 : μ = 65 , Hα : μ > 65 .

We are given that the time, in number of days, until maturity of a certain variety of tomato plant is Normally distributed, with mean μ and standard deviation s = 2.4.

You select a simple random sample of four plants of this variety and measure the time until maturity. The sample yields x bar = 65.

You read on the package of seeds that these tomatoes reach maturity, on average, in 61 days.

Now, since we know about;

sample size, n = 4

sample standard deviation, s = 2.4

sample, x bar = 65

The only line which represent information about the population mean is reading on the package of seeds that these tomatoes reach maturity, on average, in 61 days.

This shows that population mean , [tex]\mu[/tex] = 61 and in null and alternate hypothesis only population mean is tested.

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 61

Alternate Hypothesis, [tex]H_1[/tex] : [tex]\mu[/tex] > 61 { we are asked for later than expected}