Suppose that you want to decide whether the distribution of primary heating fuel of occupied housing units built after 1974 differs from that of all occupied housing units. To help you decide, you take a random sample of n housing units built after 1974 and obtain a frequency distribution of their primary heating fuel.

The primary heating fuel for all occupied housing units is distributed as follows.

Primary heating fuel Percentage
Natural gas 51.3
Fuel oil, kerosene 10.9
Electricity 29.4
Liquid propane gas 5.4
Wood 2.2
Other 0.8

a. Identify the population and variable under
consideration.

b. For each of the following sample sizes (values of n),
decide whether conducting a chi-square goodness-of-fit
test is reasonable and explain your answer.: 100, 150;
200; 250

Solution Preview

a. The population is the distribution of primary heating fuel of occupied housing units built (after 1974) and the variable is the different primary heating fuels, like Natural gas, Fuel oil, kerosene etc.

<br>b. The formula of chi-square goodness-of-fit test is:
<br> X2=SUM(Observed-Expected)^2/Expected
<br>However, two assumptions are to ...

Solution Summary

Suppose that you want to decide whether the distribution of primary heating fuel of occupied housing units built after 1974 differs from that of all occupied housing units. To help you decide, you take a random sample of n housing units built after 1974 and obtain a frequency distribution of their primary heating fuel.

The primary heating fuel for all occupied housing units is distributed as follows.

Primary heating fuel Percentage
Natural gas 51.3
Fuel oil, kerosene 10.9
Electricity 29.4
Liquid propane gas 5.4
Wood 2.2
Other 0.8

a. Identify the population and variable under
consideration.

b. For each of the following sample sizes (values of n),
decide whether conducting a chi-square goodness-of-fit
test is reasonable and explain your answer.: 100, 150;
200; 250

Is there an alternative test to the chi squared test? What if my results give an expected frequency below 5, which stats book states that these should be treated with caution? Is there a more appropriate stat test which would be more accurate in working out the significance of the results?

A) When will you use a Goodness-of-fit Chi-Square distribution?
b) What are the characteristics of chi-square distribution?
c) Do you have to follow the five step process of hypothesis testing?
d) What are the drawbacks of chi-square testing?

In a test of the independence of two variables, one the variables has two possible categories and the other has three possible categories. What will be the critical value of chi-square if the test is to be carried out at the 0.025 level? At the 0.05 level?

You run a chi-square test. The critical value for this test at the .05 level is a chi-square of 6.21. What value must your obtained chi square
statistic be in order to be considered significant at the .05 level?

a) Why do you use thechi-square statistic?
b) What type of data is used with chi square analysis?
c) What are the hypotheses in a chi-square test for independence?
d) How do we calculate the expected frequencies for each cell of a contingency table?
e) How do we calculate the degrees of freedom for an r x c contingency

The Springfield Emergency Medical Service keeps records of its calls. A study of 150 five-minute time intervals resulted in the distribution of number of calls. Use a .01 level of significance and do a chi-square goodness of fit analysis for the data. Analyze the results and interpret what they mean. Use the 5-step hypothesis te

What happens to the shape of the Chi Square distribution curve as the sample size gets larger? What about when the number of cells or groups gets larger?

Cross between pure red tomato and yellow tomato produced all red F1 progeny. From the F2 progeny of 400 plants, 90 were yellow. Hypothesize that a single pair of allele is involved such that Y- = Red and yy = Yellow. Test this hypothesis using Chi square test.

A research organization has collected the following data on household size and telephone ownership for 200 U.S. households at the 0.05 level, are the two variables independent? Based on thechi-square table, what is the most accurate statement that can be made about the p-value for the test?

Cross tabulate and do a chi-square test on the following. Is there a relationship between the two variables given? Test at the level of alpha = 0.01. Why is Chi square appropriate here? Show all working.
Smoking vs Tumour Index
Smoking
Non-smoker=0 Smoker=1
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