Question

Use the following information for Questions 1-3: At Regan's Tomato Heaven Farm, the yield per acre, measured in bushels of tomatoes, is known to follow a Normal Distribution with variance σ2 = 225.

1. A random sample is obtained with the following results:

n=16.

Sample mean X-Bar: 56.

Provide a test of null hypothesis H0: μ = 48 versus the alternative hypothesis HA: μ ≠ 48 with α = 0.05.

a. Calculated Z-Score =

b. Z-Critical =

c. Conclusion (Reject H0/Fail to Reject H0)

3. Another random sample is obtained with the following results:

n=36.

Regan would like to conduct a test of null hypothesis H0: μ = 55 versus the alternative hypothesis HA: μ < 55 with α = 0.01

a. Z-Critical =

b. X-Bar Critical. That is, at what value of X-Bar woud you reject H0:

Answer 1

Solution:

Given: At Regan's Tomato Heaven Farm, the yield per acre, measured in bushels of tomatoes, is known to follow a Normal Distribution with variance σ² = 225.

Thus

Question 1)

Sample Size = n = 16

Sample mean =

The null hypothesis H0: μ = 48 versus the alternative hypothesis HA: μ ≠ 48

Level of significance = α = 0.05.

Part a) Calculated Z-Score =........?

Part b. Z-Critical =...........?

Since this is two tailed test, find : Area =

Look in z table for area = 0.0250 or its closest area and find z value

Area 0.0250 corresponds to -1.9 and 0.06

thus z critical value = -1.96

Since this is two tailed test, we have two z critical values: ( -1.96 , 1.96)

Part c. Conclusion:

Since z test statistic value = z score = 2.13 > z critical value = 1.96, we reject H0.

Reject H0.

Thus the mean yield per acre, measured in bushels of tomatoes is different from 48.

Question 3)

Sample Size = n = 36

The null hypothesis H0: μ = 55 versus the alternative hypothesis HA: μ < 55

Level of significance = α = 0.01.

Part a) Z-Critical =...........?

Since this is left tailed test( One tailed ),

look in z table for area = 0.0100 or its closest area and find z value.

Area 0.0099 is closest to 0.0100 and it corresponds to -2.3 and 0.03

thus z critical value = -2.33

Part b) Find

We reject H0 , when z test statistic value is less than or equal to -2.33

Use following formula:

Thus we reject H0, if   

( Round answer to specified number of decimal places)