Refer to Exercises 1 and 3.
(a) Confirm that the expected counts are large enough to use a chi-square distribution. Which distribution (specify the degrees of freedom) should you use?
(b) Sketch a graph like Figure 11.4 (page 683) that shows the P-value.
(c) Use Table C to find the P-value. Then use your calculator’s C2cdf command
(d) What conclusion would you draw about the company’s claimed distribution for its deluxe mixed nuts? Justify your answer.
(a) The degree of freedom is 3 and we will use chi- square distribution.
(c) The value of is
(d) There is insufficient evidence to dismiss the company's claim.
Given in the question to refer exercise 1 and 3.
The projected counts must be large enough for the chi-square distribution to be used. We have to calculate the degree of freedom as well.
To calculate the degree of freedom, use the following formula:
Freedom of degree = number of categories.
The predicted counts can be calculated as follows:
If ALL predicted counts are at least , the expected counts are large enough to employ a chi-square distribution.
The degree of freedom is as follows:
According to the information, we know that the test statistic is .
We must create a graph that displays the p value.
From Part (a), we observed that the degree of freedom is
As a result, the Chi-square distribution with three degrees of freedom must be used. The P-value is the possibility of winning the test statistic's value, or a number that is more extreme.
According to the information,
Using a table and calculator, we must calculate the P-value.
Using the table, the value at 2 degrees of freedom is:
Let's use the Ti-83 calculator to find the value:
From the previous part, we know that the .
We must reach a conclusion regarding the company's claim.
The significance level is exceeded by the value. The null hypothesis is un rejectable. As a result, there is lack of evidence to dismiss the company's distribution claim for its deluxe mixed nuts.
Housing According to the Census Bureau, the distribution by ethnic background of the New York City population in a recent year was
The manager of a large housing complex in the city wonders whether the distribution by the race of the complex’s residents is consistent with the population distribution. To ﬁnd out, she records data from a random sample of residents. The table below displays the sample data
Are these data signiﬁcantly different from the city’s distribution by race? Carry out an appropriate test at the level to support your answer. If you ﬁnd a signiﬁcant result, perform follow-up analysis.
Reading and grades (3.2) The Fathom scatterplot below show the number of books read and the English grade for all students in the study. A least-squares regression line has been added to the graph.
(a) Interpret the meaning of the y-intercept in context.
(b) The student who reported reading books for pleasure had an English GPA of . Find this student’s residual. Show your work.
(c) How strong is the relationship between English grades and the number of books read? Give appropriate evidence to support your answer.
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