Exam 15: Chi-Squared Tests Optional

NARRBEGIN: Sales Volumes Sales Volumes A telemarketer makes five calls per day. A sample of 200 days gives the frequencies of sales volumes listed below: Number of Sales Observed Frequency (days) 0 10 1 38 2 69 3 63 4 18 5 2 Assume the population is binomial distribution with a probability of purchase p equal to 0.50.NARREND -{Sales Volumes Narrative} Should the assumption of a binomial distribution be rejected at the 5% significance level?

A large chi-squared test statistic in a test of a contingency table means you conclude:

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. Child present in car Seat Belts NO YES Worn 83 200 Not Worn 337 380 NARREND -{Seat Belts Narrative} At 5% level of significance, what is the critical value of the test statistic?

Consider a multinomial experiment involving 100 trials and 3 categories (cells). The observed frequencies resulting from the experiment are shown in the accompanying table. Categary 1 2 3 Frequency 38 35 27 Use the 5% significance level to test the hypotheses H₀: p₁ = 0.45, p₂ = 0.30, p₃ = 0.25 vs. H₁: At least two proportions differ from their specified values.

The only way the chi-squared test statistic can be zero is if the observed frequencies are all exactly the same as the expected frequencies.

When we describe a population of nominal data, with exactly two categories, the multinomial experiment is actually a binomial experiment with one of the categorical outcomes labeled "success" and the other labeled "failure".

Which test(s) can you use when you want to describe a population with two categories?

A chi-squared goodness-of-fit test is always conducted as a(n):

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. Child present in car Seat Belts NO YES Worn 83 200 Not Worn 337 380 NARREND -{Seat Belts Narrative} Prepare the table of expected values.

The chi-squared test for normality must follow the rule of ____________________ regarding expected values.

Suppose that a random sample of 150 observations was drawn from a population. After calculating the mean and standard deviation, each observation was standardized and the number of observations in each of the intervals below was counted. Can we infer at the 5% significance level that the data were drawn from a normal population? Intervals Frequency Z\leq-1.5 15 -1.51.5 13

A major insurance firm interviewed a random sample of 1,200 college students to find out the type of life insurance preferred, if any. The results follow: Insurance Preference Gender Term Whole Life No Insurance Female 100 80 325 Male 160 60 475 Is there evidence that life insurance preference of male students is different than that of female students? Test using the 5% level of significance.

If the expected frequency of a cell is less than 5, you should increase the significance level.

If we want to perform a two-tail test for differences between two populations of nominal data with exactly two categories, we can employ either the z-test of p₁ - p₂, or the chi-squared test of a contingency table.

If each element in a population is classified into one and only one of several categories, the population is:

A chi-squared distribution has a shape that is ____________________.

The number of degrees of freedom associated with the chi-squared test statistic for normality is the number of ____________________ minus 1 minus the number of ____________________ estimated.

Of the values for a chi-squared test statistic listed below, which one is most likely to lead to rejecting the null hypothesis in a goodness-of-fit test?

To address whether two variables are related in a contingency table, the null hypothesis, H₀, says that

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. Child present in car Seat Belts NO YES Worn 83 200 Not Worn 337 380 NARREND -{Seat Belts Narrative} Calculate the value of the test statistic.