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Exam 15: Chi-Squared Tests Optional

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Question 51

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In conducting a chi-squared goodness-of-fit test, an essential condition is that all expected frequencies are at least five.

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Question 52

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If we want to conduct a one-tail test of a population proportion, we can employ:

A) z-test of a population proportion.
B) the chi-squared test of a binomial experiment since z² = $\chi$ ².
C) the chi-squared test of a contingency table.
D) Both a and b

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Question 53

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Which of the following statements is true for chi-squared tests?

In 2011, Brand A MP3 Players had 45% of the market, Brand B had 35%, and Brand C had 20%. This year the makers of brand C launched a heavy advertising campaign. A random sample of electronic stores shows that of 10,000 MP3 Players sold, 4,350 were Brand A, 3,450 were Brand B, and 2,200 were Brand C. Has the market changed? Test at $\alpha$ = 0.01.

A large value of a chi-squared test statistic in a test of a contingency table leads you to conclude the two variables are ____________________.

NARRBEGIN: Seat Belts Seat Belts A study was conducted to determine whether the use of seat belts in vehicles depends on whether or not a child was present in the car. A sample of 1,000 people treated for injuries sustained from vehicle accidents was obtained, and each person was classified according to (1) child present (yes/no) and (2) seat belt usage (worn or not worn) during the accident. The data are shown in the table below. $\begin{array} { | l | c c | } & { \text { Child present in car } } \\\hline \text { Seat Belts } & \text { NO } & \text { YES } \\\hline \text { Worn } & 83 & 200 \\\text { Not Worn } & 337 & 380 \\\hline\end{array}$ NARREND -{Seat Belts Narrative} How many degrees of freedom are associated with the proper test in this experiment?

If we want to perform a one-tail test of a population proportion p, we can employ either the z-test of p, or the chi-squared goodness-of-fit test.

If the expected frequency e_i for any cell i is less than 5, we should:

In the test of a contingency table, the expected cell frequencies must satisfy the rule of 5.

The number of degrees of freedom for a contingency table with r rows and c columns is:

A sports preference poll showed the following data for adults and children: $\begin{array}{l}\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\text { Favorite Sport }\\\begin{array} { | l | c c c c c | } \hline \text { gender } & \text { Baseball } & \text { Soccer } & \text { Rugby } & \text { Hockey } & \text { Archery } \\\hline \text { Adults } & 24 & 17 & 30 & 18 & 22 \\\text { Children } & 21 & 20 & 22 & 12 & 28 \\\hline\end{array}\end{array}$ Use the 5% level of significance and test to determine whether sports preferences depend on age group.

All of the expected frequencies in a chi-squared goodness-of-fit test must be equal to each other.

Which statistical technique is appropriate when we wish to analyze the relationship between two qualitative variables with two or more categories?

The null hypothesis states that the sample data came from a normally distributed population. The researcher calculates the sample mean and the sample standard deviation from the data. The data arrangement consisted of five categories. Using $\alpha$ = 0.05, the appropriate critical value for this chi-squared test for normality is 5.99147.

The owner of a consumer products company asked a random sample of employees how they felt about the work they were doing. The following table gives a breakdown of their responses by age. Is there sufficient evidence to conclude that the level of job satisfaction is related to age? Use $\alpha$ = 0.10. $\begin{array}{l}\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\text { Rosponse }\\\begin{array} {| l | c c c | } \hline \text { Age } & \text { Very Interesting } & \text { Fairly Interestine } & \text { Not Interesting } \\\hline \text { Under 30 } & 31 & 24 & 13 \\\text { Between 30 and 50 } & 42 & 30 & 4 \\\text { Over 50 } & 32 & 21 & 3 \\\hline\end{array}\end{array}$

The squared difference between the observed and expected frequencies should be large if there is a significant difference between the proportions.

The number of degrees of freedom associated with the chi-squared test for normality is the number of intervals used minus the number of parameters estimated from the data.

NARRBEGIN: Seat Belts Seat Belts A study was conducted to determine whether the use of seat belts in vehicles depends on whether or not a child was present in the car. A sample of 1,000 people treated for injuries sustained from vehicle accidents was obtained, and each person was classified according to (1) child present (yes/no) and (2) seat belt usage (worn or not worn) during the accident. The data are shown in the table below. $\begin{array} { | l | c c | } & { \text { Child present in car } } \\\hline \text { Seat Belts } & \text { NO } & \text { YES } \\\hline \text { Worn } & 83 & 200 \\\text { Not Worn } & 337 & 380 \\\hline\end{array}$ NARREND -{Seat Belts Narrative} Which test would be used to properly analyze the data in this experiment?

Suppose that two shipping companies, A and B, each decide to estimate the annual percentage of shipments on which a $100 or greater claim for loss or damage was filed by sampling their records, and they report the data shown below. $\begin{array} { | l | c c | } \hline & \text { Company A } & \text { Company B } \\\hline \text { Total shipments sampled } & \text { 800 } & \text { 600 } \\\text { Number of shipments with a claim } \geq \$ 100 & 200 & 100 \\\hline\end{array}$ The owner of Company B is hoping to use these data to show that her company is superior to Company A with regard to the percentage of claims filed. Which test would be used to properly analyze the data in this experiment?

For a chi-squared distributed random variable with 10 degrees of freedom and a level of significance of 0.025, the chi-squared table value is 20.4831. Suppose the value of your test statistic is 16.857. This will lead you to reject the null hypothesis.