Question

Use the following for the next 5 questions: The time (in number of days) until maturity of a certain variety of hot pepper is Normally distributed, with unknown mean μ and standard deviation σ=2.4. This variety is advertised as taking 80 days to mature. Suppose you wish to test whether the number of days to mature is less than 80 days if you use a certain growing regimen. You select a simple random sample of four plants of this variety and measure the time until maturity.

The four times, in days, are
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Use a significance level of 0.05.
What is the question of interest?

A. Is the sample mean for the pepper plant less than 80 days?
B. Is the true mean different than 80 ?
C. Is there evidence the true mean time to maturity is greater than 80 days?
D. Is there evidence the average days to maturity for the pepper plant is less than 80 days?

Answer 1

The question of interest is whether the sample mean for the pepper plant is less than 80 days. This can be determined using a hypothesis test and comparing the test statistic to the critical value.Option A is the correct answer.

Step-by-step explanation:

The question of interest in this case is A. Is the sample mean for the pepper plant less than 80 days?

To determine the answer to this question, we need to use a hypothesis test. The null hypothesis (H0) states that the mean number of days to maturity is equal to 80, and the alternative hypothesis (Ha) states that the mean number of days to maturity is less than 80.

We can calculate the test statistic using the formula: t = (sample mean - population mean) / (sample standard deviation / sqrt(sample size)). Then, we compare the test statistic to the critical value from the t-distribution table with (sample size - 1) degrees of freedom at a significance level of 0.05.

If the test statistic is less than the critical value, we reject the null hypothesis and conclude that there is evidence the average days to maturity for the pepper plant is less than 80 days.