The offspring

produced by a cross between two given types of plants can be any of the three

genotypes denoted by A, B, C and D. A theoretical model of gene inheritance

suggests that the offspring of types A, B, C and D should be in the ratio 1:1:1:2.

For experimental verification, 150 plants are bred by crossing the two given

types. Their genetic classifications are recorded as below. Do these data

contradict the genetic model? Test at α=0.05. 

The U.S. Department of Agriculture (USDA) uses sample surveys to produce important economic estimates. One pilot study used samples of sales across the USA from two different months to estimate average wheat prices. Below are the summary statistics, in dollars per bushel, for these two months. Can we claim a difference between the mean prices in the two months?

a. Construct a suitable 95% confidence interval to determine if there is a difference between the mean prices in the two months. Give your full solutions. [4 marks]

b. With 95% confidence, can we claim a difference between the mean prices in the two months? Explain why. [1 mark]

c. Test at 5% if there is a difference between the mean prices in the two months. [9 marks]

d. Are the conclusions from the confidence interval and the significance test the same? Explain why or why not. [1 mark]

The value of the test statistic is

The null hypothesis is

The alternative hypothesis is

The p-value for this test is

The conclusion of this test, based on a significance level of 0.05, is

What is the standard deviation of the sampling distribution of all sample proportions, for this size?

What is the mean of the sampling distribution of all sample proportions, for this size?