In a certain school district, it was observed that 33% of the students in the element schools were classified as only children (no siblings). However, in the special program for talented and gifted children, 140 out of 354 students are only children. The school district administrators want to know if the proportion of only children in the special program is significantly different from the proportion for the school district. Test at the α=0.01 level of significance.What is the hypothesized population proportion for this test?p=(Report answer as a decimal accurate to 2 decimal places. Do not report using the percent symbol.)Based on the statement of this problem, how many tails would this hypothesis test have? one-tailed test two-tailed test Choose the correct pair of hypotheses for this situation: (A) (B) (C) H0:p=0.33H0:p=0.33Ha:p<0.33Ha:p<0.33 H0:p=0.33H0:p=0.33Ha:p≠0.33Ha:p≠0.33 H0:p=0.33H0:p=0.33Ha:p>0.33Ha:p>0.33 (D) (E) (F) H0:p=0.395H0:p=0.395Ha:p<0.395Ha:p<0.395 H0:p=0.395H0:p=0.395Ha:p≠0.395Ha:p≠0.395 H0:p=0.395H0:p=0.395Ha:p>0.395Ha:p>0.395 (A) (B) (C) (D) (E) (F) Using the normal approximation for the binomial distribution (without the continuity correction), what is the test statistic for this sample based on the sample proportion?z=(Report answer as a decimal accurate to 3 decimal places.)You are now ready to calculate the P-value for this sample.P-value = (Report answer as a decimal accurate to 4 decimal places.)This P-value (and test statistic) leads to a decision to... reject the null accept the null fail to reject the null reject the alternative As such, the final conclusion is that... There is sufficient evidence to warrant rejection of the assertion that there is a different proportion of only children in the G&T program. There is not sufficient evidence to warrant rejection of the assertion that there is a different proportion of only children in the G&T program. The sample data support the assertion that there is a different proportion of only children in the G&T program. There is not sufficient sample evidence to support the assertion that there is a different proportion of only children in the G&T program.
Compound Probability
Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent.
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Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described.
Conditional Probability
By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.
In a certain school district, it was observed that 33% of the students in the element schools were classified as only children (no siblings). However, in the special program for talented and gifted children, 140 out of 354 students are only children. The school district administrators want to know if the proportion of only children in the special program is significantly different from the proportion for the school district. Test at the α=0.01 level of significance.
What is the hypothesized population proportion for this test?
p=
(Report answer as a decimal accurate to 2 decimal places. Do not report using the percent symbol.)
Based on the statement of this problem, how many tails would this hypothesis test have?
- one-tailed test
- two-tailed test
Choose the correct pair of hypotheses for this situation:
| (A) | (B) | (C) |
|---|---|---|
| H0:p=0.33H0:p=0.33 Ha:p<0.33Ha:p<0.33 |
H0:p=0.33H0:p=0.33 Ha:p≠0.33Ha:p≠0.33 |
H0:p=0.33H0:p=0.33 Ha:p>0.33Ha:p>0.33 |
| (D) | (E) | (F) |
| H0:p=0.395H0:p=0.395 Ha:p<0.395Ha:p<0.395 |
H0:p=0.395H0:p=0.395 Ha:p≠0.395Ha:p≠0.395 |
H0:p=0.395H0:p=0.395 Ha:p>0.395Ha:p>0.395 |
Using the normal approximation for the binomial distribution (without the continuity correction), what is the test statistic for this sample based on the sample proportion?
z=
(Report answer as a decimal accurate to 3 decimal places.)
You are now ready to calculate the P-value for this sample.
P-value =
(Report answer as a decimal accurate to 4 decimal places.)
This P-value (and test statistic) leads to a decision to...
- reject the null
- accept the null
- fail to reject the null
- reject the alternative
As such, the final conclusion is that...
- There is sufficient evidence to warrant rejection of the assertion that there is a different proportion of only children in the G&T program.
- There is not sufficient evidence to warrant rejection of the assertion that there is a different proportion of only children in the G&T program.
- The sample data support the assertion that there is a different proportion of only children in the G&T program.
- There is not sufficient sample evidence to support the assertion that there is a different proportion of only children in the G&T program.
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