In: Statistics and Probability

Many elementary school students in a school district currently have ear infections. A random sample of children in two different schools found that 21 of 42 at one school and 15 of 35 at the other had this infection. Conduct a test to answer if there is sufficient evidence to conclude that a difference exists between the proportion of students who have ear infections at one school and the other. Find the test statistic.

*Let P _{1} be the proportion of students who have ear
infections at one school,*

*and P _{2} be the proportion of students who have ear
infections at other school.*

**Hypothesis :**

v/s

**Given data :**

X_{1}=21

n_{1}=42

X_{2}=15

n_{2}=35

**Sample proprotions are**

**Pooled proportions:**

**Test statistics :**

**P value :**Is the value of the lowets level of
singnificance at which we could reject the Null hypothesis
H_{0}

**P value at 5% los**

P value = 0.5318 > 0.5

Failed to Reject the null hypothesis and result is not significant

Salaries for teachers in a particular elementary school district
have a mean of $44,000 and a standard deviation of $6,500. We
randomly survey 36 teachers from that district.
Why can we say the sampling distribution of mean salaries for
teachers in this district is approximately normal?
Find the probability that the mean salary is less than
$43,000.
Find the probability that the mean salary is between $45,000
and $47,000.

The ages? (in years) of a random sample of elementary school
kids are shown. Determine the? range, variance, and standard
deviation of the sample data set. 5 7 9 6 7 8

A random sample of elementary school children in New York state
is to be selected to estimate the proportion p p who have received
a medical examination during the past year. It is desired that the
sample proportion be within 0.045 of the true proportion with a 98
98 % level of confidence (a) Assuming no prior information about p
p is available, approximately how large of a sample size is
needed?
If a planning study indicates that pp is...

A sample of 52 Elementary Statistics students includes 13 women.
Assuming the sample is random:
(a) Estimate the percentage of women taking Elementary
Statistics by computing an appropriate confidence interval with 98%
confidence.
(b) At 10% significance, test whether less than 40% of the
enrollment in all Elementary Statistics classes consists of
women.

If a school district takes a random sample of 74 Math SAT scores
and finds that the average is 490, and knowing that the population
standard deviation of Math SAT scores is intended to be 100. Find a
99% confidence interval for the mean math SAT score for this
district.
≤μ≤

1. A random sample of 64 second graders in a certain school
district are given a standardized mathematics skills test. The
sample mean score is 51.58. Assume the standard deviation for the
population of test scores is 15. The nationwide average score on
this test us 50. The school superintendent wants to know whether
the second graders in her school district have greater math skills
than the nationwide average. Perform the hypothesis test and
compute the P value. Based on...

If a school district takes a random sample of 51 Math SAT scores
and finds that the average is 464, and knowing that the population
standard deviation of Math SAT scores is intended to be 100. Find a
99% confidence interval for the mean math SAT score for this
district.
≤ μ ≤

If a school district takes a random sample of 78 Math SAT scores
and finds that the average is 461, and knowing that the population
standard deviation of Math SAT scores is intended to be 100. Find a
99% confidence interval for the mean math SAT score for this
district.
≤μ≤

1)
A random sample of 64 second- graders in a certain school district
are given a standardized mathematics skills test. The sample mean
score is 51.60. Assume the standard deviation for the population of
test scores is 15. The nationwide average score on this test is 50.
The school superintendent wants to know whether the second-graders
in her school district have greater math skills than the nationwide
average. Perform the hypothesis test and compute the p -value.
Write down your...

Salaries for teachers in a particular elementary school district
are normally distributed with a mean of $44,000 and a
standard deviation of $6,500. We randomly survey ten teachers from
that district.
1.Find the probability that the teachers earn a total of over
$400,000
2.If we surveyed 70 teachers instead of ten, graphically, how
would that change the distribution in part d?
3.If each of the 70 teachers received a $3,000 raise,
graphically, how would that change the distribution in part...

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