Life on Other Planets Forty-three percent of people believe that there is life on other planets in the universe. A scientist does not agree with this finding. He surveyed 110 randomly selected individuals and found 44 believed that there is life on other planets. At a = 0.05, is there sufficient evidence to conclude that the percentage differs from 43%? Use the critical value method with tables. Do not round intermediate steps. Part: 0 / 5 Part 1 of 5 (a) State the hypotheses and identify the claim. Ho : (Choose one) ▼ H : (Choose one) ▼ This hypothesis test is a (Choose one) ▼ test.

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Chapter1: Starting With Matlab
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Sample Question
Life on Other Planets Forty-five percent of people believe that there is life on other planets in the universe. A
scientist does not agree with this finding. He surveyed 125 randomly selected individuals and found 50 believed that
there is life on other planets. At a-0.10, is there sufficient evidence to conclude that the percentage differs from
45%? Use the critical value method with tables. Do not round intermediate steps.
(a) State the hypotheses and identify the claim.
(b) Find the critical value(s).
(c) Compute the test value.
(d) Make the decision.
(e) Summarize the results.
Explanation
(a) State the hypotheses and identify the claim.
The null hypothesis H, is the statement that there is no difference between a parameter and a specific value. This is
equivalent to H:p-0.45.
The alternative hypothesis H, is the statement that there is a difference between a parameter and a specific value.
In this case, the percentage of people who believe that there is life on other planets differs from 45%. This is
equivalent to H, :p+0.45.
The problem asks, "Can it be concluded that the percentage of people who believe that there is life on other planets
differs from 45%?"
Hence, the claim is the alternative hypothesis.
(b) Find the critical value(s).
From the figure below, for a two-tailed test with a= 0.10, the critical values are z=t1.65.
a-0.10, C.V. -±1.65
Y=d:
a=0.05, C.V. =±1.96
a= 0.01, C.V. =±2.58
(c) Compute the test value.
Formula for the : Test for Proportions
Vpg'n
where p
sample proportion
p- population proportion
n = sample size
First, it is necessary to find p,p, and q.
50
125
-0.4
p- 45%
- 0.45
- 1-0.45
- 0.55
Using the formula for the z-test for proportions, compute the test value.
0.4 -0.45
V(0.45)(0.55)/125
--L.12
Hence, the test value, rounded to 2 decimal places, is :--1.12.
(d) Make the decision.
Since the test value does not fall in the critical region, do not reject the null hypothesis.
- 1.65 - 1.12 0
1.65
(e) Summarize the results.
Since the null hypothesis was not rejected, tharei not onouah auidence to cunnort the caim that the porcantane of
people who believe that there is life on other planets differs from 45%.
Transcribed Image Text:Sample Question Life on Other Planets Forty-five percent of people believe that there is life on other planets in the universe. A scientist does not agree with this finding. He surveyed 125 randomly selected individuals and found 50 believed that there is life on other planets. At a-0.10, is there sufficient evidence to conclude that the percentage differs from 45%? Use the critical value method with tables. Do not round intermediate steps. (a) State the hypotheses and identify the claim. (b) Find the critical value(s). (c) Compute the test value. (d) Make the decision. (e) Summarize the results. Explanation (a) State the hypotheses and identify the claim. The null hypothesis H, is the statement that there is no difference between a parameter and a specific value. This is equivalent to H:p-0.45. The alternative hypothesis H, is the statement that there is a difference between a parameter and a specific value. In this case, the percentage of people who believe that there is life on other planets differs from 45%. This is equivalent to H, :p+0.45. The problem asks, "Can it be concluded that the percentage of people who believe that there is life on other planets differs from 45%?" Hence, the claim is the alternative hypothesis. (b) Find the critical value(s). From the figure below, for a two-tailed test with a= 0.10, the critical values are z=t1.65. a-0.10, C.V. -±1.65 Y=d: a=0.05, C.V. =±1.96 a= 0.01, C.V. =±2.58 (c) Compute the test value. Formula for the : Test for Proportions Vpg'n where p sample proportion p- population proportion n = sample size First, it is necessary to find p,p, and q. 50 125 -0.4 p- 45% - 0.45 - 1-0.45 - 0.55 Using the formula for the z-test for proportions, compute the test value. 0.4 -0.45 V(0.45)(0.55)/125 --L.12 Hence, the test value, rounded to 2 decimal places, is :--1.12. (d) Make the decision. Since the test value does not fall in the critical region, do not reject the null hypothesis. - 1.65 - 1.12 0 1.65 (e) Summarize the results. Since the null hypothesis was not rejected, tharei not onouah auidence to cunnort the caim that the porcantane of people who believe that there is life on other planets differs from 45%.
Life on Other Planets Forty-three percent of people believe that there is life on other planets in the universe. A scientist
does not agree with this finding. He surveyed 110 randomly selected individuals and found 44 believed that there is life on
other planets. At a = 0.05, is there sufficient evidence to conclude that the percentage differs from 43%? Use the critical
value method with tables. Do not round intermediate steps.
Part: 0 / 5
Part 1 of 5
(a) State the hypotheses and identify the claim.
H :
(Choose one) ▼
H :
(Choose one)
This hypothesis test is a (Choose one) ▼
test.
Transcribed Image Text:Life on Other Planets Forty-three percent of people believe that there is life on other planets in the universe. A scientist does not agree with this finding. He surveyed 110 randomly selected individuals and found 44 believed that there is life on other planets. At a = 0.05, is there sufficient evidence to conclude that the percentage differs from 43%? Use the critical value method with tables. Do not round intermediate steps. Part: 0 / 5 Part 1 of 5 (a) State the hypotheses and identify the claim. H : (Choose one) ▼ H : (Choose one) This hypothesis test is a (Choose one) ▼ test.
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