About 10% of the human population is left-handed. Suppose a researcher speculates that artists are more likely to be left-handed than other people in the general population. The researcher surveys 200 artists and finds that 26 of them are left-handed. If we use p to represent the proportion of all artists who are left-handed, the hypotheses are Ho: p = 0.10 and Ha: p > 0.10. The sample result was that 26 artists of 200 surveyed (or 13%) are left- handed. ЛUSE SALT (a) From the given information, do we know if the conditions necessary to use a z-statistic for this test are met? Explain. We are not sure the sample was selected randomly, the sample size is large enough because both np and n(1 - p) are greater than or equal to 10. (b) State the population of interest, the population parameter of interest, and the value of the sample statistic. The population of interest is artists . The population parameter is p = the proportion of artists who are left handed (c) Conduct a hypothesis test using level of significance α = 0.05. Clearly give the details of the five steps. Be sure to write a conclusion. P < × 0.1 Set up the null and alternative hypothesis. '0' a H: P > 0.1 Compute the test statistics for this situation. (Round your answer to two decimal places.) Z = Calculate the p-value for the test. (Round your answer to four decimal places.) p-value = The sample statistic is
About 10% of the human population is left-handed. Suppose a researcher speculates that artists are more likely to be left-handed than other people in the general population. The researcher surveys 200 artists and finds that 26 of them are left-handed. If we use p to represent the proportion of all artists who are left-handed, the hypotheses are Ho: p = 0.10 and Ha: p > 0.10. The sample result was that 26 artists of 200 surveyed (or 13%) are left- handed. ЛUSE SALT (a) From the given information, do we know if the conditions necessary to use a z-statistic for this test are met? Explain. We are not sure the sample was selected randomly, the sample size is large enough because both np and n(1 - p) are greater than or equal to 10. (b) State the population of interest, the population parameter of interest, and the value of the sample statistic. The population of interest is artists . The population parameter is p = the proportion of artists who are left handed (c) Conduct a hypothesis test using level of significance α = 0.05. Clearly give the details of the five steps. Be sure to write a conclusion. P < × 0.1 Set up the null and alternative hypothesis. '0' a H: P > 0.1 Compute the test statistics for this situation. (Round your answer to two decimal places.) Z = Calculate the p-value for the test. (Round your answer to four decimal places.) p-value = The sample statistic is
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 10CYU
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Transcribed Image Text:About 10% of the human population is left-handed. Suppose a researcher speculates that artists are more likely to be left-handed than other people in the general population. The researcher surveys
200 artists and finds that 26 of them are left-handed.
If we use p to represent the proportion of all artists who are left-handed, the hypotheses are Ho: p = 0.10 and Ha: p > 0.10. The sample result was that 26 artists of 200 surveyed (or 13%) are left-
handed.
ЛUSE SALT
(a) From the given information, do we know if the conditions necessary to use a z-statistic for this test are met? Explain.
We are not
sure the sample was selected randomly, the sample size is
large enough because both np and n(1 - p) are greater than or equal to
10.
(b) State the population of interest, the population parameter of interest, and the value of the sample statistic.
The population of interest is artists
.
The population parameter is p = the proportion of artists who are left handed
(c) Conduct a hypothesis test using level of significance α = 0.05. Clearly give the details of the five steps. Be sure to write a conclusion.
P < × 0.1
Set up the null and alternative hypothesis.
'0'
a
H: P
>
0.1
Compute the test statistics for this situation. (Round your answer to two decimal places.)
Z =
Calculate the p-value for the test. (Round your answer to four decimal places.)
p-value
=
The sample statistic is
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