The time (in number of days) until maturity of a certain variety of tomato plant is Normally distributed with mean μ and standard deviation σ = 2.4. I select a simple random sample of four plants of this variety and measure the time until maturity. The sample yields = 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: H0: μ = 65, Ha: μ 65. H0: μ = 61, Ha: μ > 61. H0: μ = 61, Ha: μ < 61.

Question

Zain Cruz

Mathematics

5 July, 09:47

The time (in number of days) until maturity of a certain variety of tomato plant is Normally distributed with mean μ and standard deviation σ = 2.4. I select a simple random sample of four plants of this variety and measure the time until maturity. The sample yields = 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: H0: μ = 65, Ha: μ 65. H0: μ = 61, Ha: μ > 61. H0: μ = 61, Ha: μ < 61.

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Keshawn Rush · Answer 1

The expected result for a normally distributed sample is

mean, mu = 61

Std. deviation, sigma = 2.4

We have a random which indicates a mean of = 65.

To test the hypothesis that the sample is too old.

The null hypothesis is

H0: mu = 61

The alternate hypothesis is

Ha: mu > 61