Question

3. (9 points) Suppose we are interested in learning about the average crop yield of wheat when adding a new change to the soil conditions. To do so, we formed 25 plots of land and measured the total yield per plot in kg. We will assume that $X_1,..., X_{25}$ follow the normal distribution with an unknown mean $\mu$ and standard deviation of 1 ton. Suppose we wish to test $H_0: \mu = 4$ tons, and $H_A: \mu > 4$ tons at level $\alpha = 0.05$. (a) (3 points) Do we need the $X_i$'s to be normally distributed in order to conduct the appropriate hypothesis test in this case? And should we conduct a T or Z test? (b) (6 points) Suppose we define a hypothesis test by the rejection region where we reject the null hypothesis $H_0$ when $\bar{X} > 5$ tons. What is the significance level of this new test?

          3. (9 points) Suppose we are interested in learning about the average crop yield of wheat when adding a
new change to the soil conditions. To do so, we formed 25 plots of land and measured the total yield
per plot in kg. We will assume that $X_1,..., X_{25}$ follow the normal distribution with an unknown mean
$\mu$ and standard deviation of 1 ton. Suppose we wish to test $H_0: \mu = 4$ tons, and $H_A: \mu > 4$ tons at
level $\alpha = 0.05$.
(a) (3 points) Do we need the $X_i$'s to be normally distributed in order to conduct the appropriate
hypothesis test in this case? And should we conduct a T or Z test?
(b) (6 points) Suppose we define a hypothesis test by the rejection region where we reject the null
hypothesis $H_0$ when $\bar{X} > 5$ tons. What is the significance level of this new test?

3. (9 points) Suppose we are interested in learning about the average crop yield of wheat when adding a
new change to the soil conditions. To do so, we formed 25 plots of land and measured the total yield
per plot in kg. We will assume that X1,..., X25 follow the normal distribution with an unknown mean
μ and standard deviation of 1 ton. Suppose we wish to test H0: μ = 4 tons, and HA: μ > 4 tons at
level α = 0.05.
(a) (3 points) Do we need the Xi's to be normally distributed in order to conduct the appropriate
hypothesis test in this case? And should we conduct a T or Z test?
(b) (6 points) Suppose we define a hypothesis test by the rejection region where we reject the null
hypothesis H0 when X̅ > 5 tons. What is the significance level of this new test?

Added by Iker R.

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