Question

In a certain school district, it was observed that 31% of the
students in the element schools were classified as only children
(no siblings). However, in the special program for talented and
gifted children, 106 out of 289 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=0.05α=0.05 level of significance.

What is the hypothesized population proportion for this test?

p=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=0.31H0:p=0.31 Ha:p<0.31Ha:p<0.31 |
H0:p=0.31H0:p=0.31 Ha:p≠0.31Ha:p≠0.31 |
H0:p=0.31H0:p=0.31 Ha:p>0.31Ha:p>0.31 |

(D) | (E) | (F) |

H0:p=0.367H0:p=0.367 Ha:p<0.367Ha:p<0.367 |
H0:p=0.367H0:p=0.367 Ha:p≠0.367Ha:p≠0.367 |
H0:p=0.367H0:p=0.367 Ha:p>0.367Ha:p>0.367 |

(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=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.

LicensePoints possible: 1

This is attempt 1 of 5.

Answer #1

TOPIC:Test for the population proportion.

In a certain school district, it was observed that 31% of the
students in the element schools were classified as only children
(no siblings). However, in the special program for talented and
gifted children, 78 out of 215 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=0.01α=0.01 level of significance.
What is the hypothesized...

In a certain school district, it was observed that 25% of the
students in the element schools were classified as only children
(no siblings). However, in the special program for talented and
gifted children, 114 out of 386 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=0.05
level of significance.
What is the hypothesized...

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, 92 out of 246 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=0.02α=0.02 level of
significance.
What is the hypothesized population proportion...

In a certain school district, it was observed that 26% of the
students in the element schools were classified as only children
(no siblings). However, in the special program for talented and
gifted children, 138 out of 425 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=0.01α=0.01 level of significance.
What is the hypothesized...

In a certain school district, it was observed that 29% of the
students in the element schools were classified as only children
(no siblings). However, in the special program for talented and
gifted children, 91 out of 257 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=0.02α=0.02 level of significance.
What is the hypothesized...

In a certain school district, it was observed that 26% of the
students in the element schools were classified as only children
(no siblings). However, in the special program for talented and
gifted children, 93 out of 313 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 = 0.05
level of significance.
What is...

in a certain school district, it was observed that 28% of the
students in the element schools were classified as only children
(no siblings). However, in the special program for talented and
gifted children, 98 out of 272 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 = 0.02
level of significance. What is...

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, 107 out of 287 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 ? = 0.05
level of significance.
H0:p=0.33
Ha:p?0.33...

In a certain school district, it was observed that 31% of the
students in the element schools were classified as only children
(no siblings). However, in the special program for talented and
gifted children, 77 out of 204 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=0.05α=0.05 level of significance.
Using the normal approximation...

7.
You wish to test the following at a significance level of
α=0.05α=0.05.
H0:p=0.85H0:p=0.85
H1:p>0.85H1:p>0.85
You obtain a sample of size n=250n=250 in which there are 225
successful observations.
For this test, we use the normal distribution as an approximation
for the binomial distribution.
For this sample...
The test statistic (zz) for the data = (Please show
your answer to three decimal places.)
The p-value for the sample = (Please show your
answer to four decimal places.)
The p-value is...
greater than...

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