Reading Errors

Refer to the Reading Errors data from Test 2.

Test the null hypothesis that the distribution of types of errors is the same for each of the three groups of readers. State your conclusion. ("Reject H ₀ " is not a sufficient conclusion.)

Do the differences among the three groups in terms of types of errors made appear to be pronounced enough that different sorts of reading drills might be warranted for the three groups?

A study (Kottmeyer, 1959) of reading errors made by second-grade pupils was carried out in order to help decide whether the use of different sorts of drills for pupils of different reading abilities is warranted. Errors were categorized as follows:

• DK: did not know the word at all
• C: substitution of a word of similar configuration (e.g., "bad" for "had")
• T: substitution of a synonym suggested by the context
• OS: other substitution

The children had been clustered into three relatively homogeneous reading groups on the basis of (1) their reading achievement scores at the end of the first grade, (2) their verbal IQs, and (3) the opinions of their first grade teachers. The three groups of children each chose the name of an animal as their group name. It happened that the least able readers chose the name Squirrels, the most able readers close the name Cats, and the middle group called themselves Bears. There were five Squirrels, nine Bears, and 11 Cats.

The numbers of errors of each type made by each child were added to obtain the group totals in the table below. The numbers of errors are not directly comparable: not only are the group sizes different, but the more able group used more difficult texts and read more.

HERE IS TABLE OF READING AREAS.

***** Distribution of Reading Errors for Three Ability Groups **********

1. Compare, in tabular form, the three groups in terms of the types of errors made.

In order to compare the three groups, a percentage distribution must be constructed:

Birth Days and Death Days

One might think that how long a person survives beyond a birthday is a random event such that each day or week or month of death (within a year) beyond the birthday is equally likely. In particular, in some specified population, it is expected that the probability of the death of an individual occurring the first month after a birthday should be 1/12, and so on. However, a person in a situation where death is not unlikely might stave off death; that is, reduce the probability of death shortly before the birthday.

Phillips (1972) investigated the tendency of famous people to survive until their next birthdays. Using a number of anthologies of famous people, he noted that such people are least likely to die in the month before their birth month; there is a dip in the death rates corresponding to the month before the birth month. Correspondingly, there is an apparent rise in the death rate in the months immediately following the birth month.

Some data are given below. Are the observed frequencies consistent with the hypothesis of probability of death of 1/12 for each month?

Airfreight Breakage

A substance used in biological and medical research is shipped by air freight to users in cartons of 1,000 ampules. The data below, involving 10 shipments, were collected on the number of times the carton was transferred from one aircraft to another over the shipment route and the number of ampules found to be broken upon arrival.

1. Plot the data. Does the number of transfers appear to affect the number of broken ampules?
   
2. Assuming that a linear model is appropriate, state the equation relating breakage to number of transfers.
   
3. Test the research hypothesis that the number of ampules broken increases with the number of times the shipment is transferred, for all shipments made by this supplier.
   
4. What does the intercept of the equation tell you about the number of broken ampules and the number of transfers?
   
5. What does the slope of the equation tell you about the number of broken ampules and the number of transfers?
   
6. Give a 95% confidence interval on the additional number of broken ampules expected with each additional transfer.
   
7. Estimate the mean number of broken ampules for shipment which are transferred once. Use a 95% confidence interval.
   
8. A special shipment will have to be transferred 4 times. Using the available data, give an estimate of the likely (95%) largest number of ampules which might be broken.

Composition of Police Force

A certain community has a population that is 72% non-Hispanic white, 22% African-American, and 6% of Hispanic origin. The 40-member police force includes 34 white officers and 4 African-American officers.

Is the composition of the police force consistent with the random recruitment model?

Single-Parent Families

Among 114 low income families, 72 were single-parent families. Among 414 non-low income families, 75 were single parent families.

Estimate the difference in proportions of single-parent families in low and non-low income families in the population from which these data were taken. Use a 95% confidence interval.

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