Question

The time (in number of days) until maturity of a certain variety of tomato plant is normally distributed with mean = 30 days to mature and standard deviation = 2.4. I select a simple random sample of four plants of this variety and measure the time until maturity. The four times, in days, are: 39, 36, 32, 33.
Conduct the hypotheses test and state the conclusion at 0.1significance level of the test if the maturity time is more than claimed.

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Answer 1

Here, we have to use one sample z test for the population mean.

The null and alternative hypotheses are given as below:

H0: the maturity time is equal to claimed value of 30 days.

Ha: the maturity time is more than claimed value of 30 days.

H0: µ = 30 versus Ha: µ > 30

This is an upper tailed test.

The test statistic formula is given as below:

Z = (Xbar - µ)/[σ/sqrt(n)]

From given data, we have

µ = 30

Xbar = 35

σ = 2.4

n = 4

α = 0.1

Critical value = 1.2816

(by using z-table or excel)

Z = (35 – 30)/[2.4/sqrt(4)]

Z = 4.1667

P-value = 0.0000

(by using Z-table)

P-value < α = 0.10

So, we reject the null hypothesis

There is sufficient evidence to conclude that the maturity time is more than claimed value of 30 days.