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Pearson online homework chapter 8 Question and answers rated A+ 2023
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Pearson online homework chapter 8UCO says that 15% of its students recieved flu shots last year. A random sample of
1000 UCO students found that 120 recieved flu shots this year.
1. Find a 95% confidence interval for the proportion of students that recieved a flu shot
this year. Round your answers to four decimal places.
2. There is enough evidence to show that the proportion of UCO students who recieved
flu shots this year has changed from last year because 0.15 is not in the confidence
interval. - correct answer 1. use condidence interval equation to get the interval:
p̂ ± Z α/2 √ p^ q^/n
Confidence interval= 0.12 ± 1.960 √ (0.12)(0.88)/1000
(0.0999,0.1401)
2. true
A genetic experiment involving peas yielded one sample of offspring consisting of
445 green peas and
157 yellow peas. Use a
0.01 significance level to test the claim that under the same circumstances,
25% of offspring peas will be yellow. Identify the null hypothesis, alternative hypothesis,
test statistic, P-value, conclusion about the null hypothesis, and final conclusion that
addresses the original claim. Use the P-value method and the normal distribution as an
approximation to the binomial distribution.
a.) What are the null and alternative hypotheses?
b.) What is the test statistic? Z=
c.)What is the P-value
d.)What is the conclusion about the null hypothesis?
e.)What is the final conclusion? - correct answer a.) H0: p= 0.25
H1: p ≠ 0.25
b.) p̂= x/n
Z= (p̂- p)/ √ (pq/ n)
p=157/ 445+157= 0.2607
z= 0.2607-0.25/ (0.25)(0.75)/445+157 = 0.61 **
, c.) p( Z>0.61)=
d.) Fail to reject the null hypothesis because the P-value is greater than the significance
level,
alpha.
E.) There is not sufficient evidence to warrant rejection of the claim that
24% of offspring peas will be yellow.
a.) Suppose you wanted to purchase a new car that had low gas mileage and you heard
on an advertisment that the Hyundai Elantra made 32 miles per gallon on average. You
purchased a Hyundai Elantra and it only made 29 miles per gallon. Is this enough proof
that Hyundai Elantra's advertisement is false?
b.)Now suppose you randomly selected 30 Hyundai Elantra's and found the average
gas mileage for the cars was 29 mpg. Because the average is less than 32, is this
enough proof that Hyundai Elantra's advertisement is false?
c.) This is where hypothesis testing comes in. The hypotheses test determines (using
probability theory) whether your mean is different enough to reject the null in favor of the
alternative hypothesis.
So for our example our alternative hypothesis (claim) would be:
d.) We would use the mean and standard deviation to calculate a test statistic and p-
value. The p-value for this problem would be the probability that we would calculate a
sample mean of 29 when the true population mean is 32 mpg. If the probability is very
small (less than our significance level (0.05)), then we would reject the null in favor of
our alternative hypothesis. This is because it is unlikely (improbable) that we would
calculate a sample mean of 29 when the true population mean is 32 based on our
calculations. If we did our sampling correctly, then we have reasonable proof that the
average miles per gallon of Hyundai Elantra's is less than 32 mpg and we can conclude:
- correct answer a.)no" as 1 car is not a big enough sample size.
b.) The average you calculated is a sample mean that has variability. If you selected a
different sample, you may find that the average is 35 mpg depending on how much
variability your sample has.
This is where hypothesis testing comes in
c.) H1:μ<32
d.) There is sufficient evidence to support the claim that Hyundai Elantra's make less
than 32 mpg
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