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It is believed that 11% of all Americans are left-handed. A college needs to know how many left-handed desks to place in the big lecture halls being constructed on its campus. In a random sample of 240 students of its 24565 students, 31 were left-handed. Does this provide enough evidence to show that students at this college have a higher percentage of left-handers than the general American population? Use a 9% level of significance.P: PARAMETER     What is the correct parameter symbol for this problem?          What is the wording of the parameter in the context of this problem?     H: HYPOTHESES     Fill in the correct null and alternative hypotheses:     𝐻0:      𝐻𝐴: A: ASSUMPTIONS     Since information was collected from each object, what conditions do we need to check?     Check all that apply.     𝑛≥30 or normal population.𝑛𝑝≥10σσ is known.𝑛(1-𝑝̂)≥10𝑁≥20𝑛σσ is unknown.𝑛(1-𝑝)≥10𝑛(𝑝̂)≥10     Check those assumptions:          1. 𝑛𝑝 = which is           2. 𝑛(1-𝑝) = which is           3. 𝑁 = which is               If no N is given in the problem, use 1000000N: NAME THE PROCEDURE     The conditions are met to use a .T: TEST STATISTIC     The symbol and value of the random variable on this problem are as follows:     Leave this answer as a fraction.     =      The formula set up of the test statistic is as follows.:       (Leave any values that were given as fractions as fractions) 𝑧=𝑝̂-𝑝𝑝(1-𝑝)𝑛=( - )/(( ⋅(1- )) / )       Final answer for the test statistic from technology.     Round to 2 decimal places:     z = O: OBTAIN THE P-VALUE     Report to 4 decimal places.     It is possible when rounded that a p-value is 0.0000     P-value = M: MAKE A DECISION     Since the p-value , we .S: STATE A CONCLUSION    There significant evidence to conclude

Question

It is believed that 11% of all Americans are left-handed. A college needs to know how many left-handed desks to place in the big lecture halls being constructed on its campus. In a random sample of 240 students of its 24565 students, 31 were left-handed. Does this provide enough evidence to show that students at this college have a higher percentage of left-handers than the general American population? Use a 9% level of significance.P: PARAMETER     What is the correct parameter symbol for this problem?          What is the wording of the parameter in the context of this problem?     H: HYPOTHESES     Fill in the correct null and alternative hypotheses:     𝐻0:      𝐻𝐴: A: ASSUMPTIONS     Since information was collected from each object, what conditions do we need to check?     Check all that apply.     𝑛≥30 or normal population.𝑛𝑝≥10σσ is known.𝑛(1-𝑝̂)≥10𝑁≥20𝑛σσ is unknown.𝑛(1-𝑝)≥10𝑛(𝑝̂)≥10     Check those assumptions:          1. 𝑛𝑝 = which is           2. 𝑛(1-𝑝) = which is           3. 𝑁 = which is               If no N is given in the problem, use 1000000N: NAME THE PROCEDURE     The conditions are met to use a .T: TEST STATISTIC     The symbol and value of the random variable on this problem are as follows:     Leave this answer as a fraction.     =      The formula set up of the test statistic is as follows.:       (Leave any values that were given as fractions as fractions) 𝑧=𝑝̂-𝑝𝑝(1-𝑝)𝑛=( - )/(( ⋅(1- )) / )       Final answer for the test statistic from technology.     Round to 2 decimal places:     z = O: OBTAIN THE P-VALUE     Report to 4 decimal places.     It is possible when rounded that a p-value is 0.0000     P-value = M: MAKE A DECISION     Since the p-value , we .S: STATE A CONCLUSION    There significant evidence to conclude

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Solution

P: PARAMETER

  • The correct parameter symbol for this problem is p p .
  • The wording of the parameter in the context of this problem is: the proportion of left-handed students at this college.

H: HYPOTHESES

  • Null hypothesis (H0 H_0 ): p=0.11 p = 0.11
  • Alternative hypothesis (HA H_A ): p>0.11 p > 0.11

A: ASSUMPTIONS

  • Since information was collected from each object, the conditions we need to check are:

    • n≥30 n \geq 30 or normal population.
    • n⋅p≥10 n \cdot p \geq 10
    • n⋅(1−p)≥10 n \cdot (1 - p) \geq 10
    • N≥20n N \geq 20n

  • Check those assumptions:

    1. n⋅p=240⋅0.11=26.4 n \cdot p = 240 \cdot 0.11 = 26.4 , which is greater than 10.
    2. n⋅(1−p)=240⋅(1−0.11)=240⋅0.89=213.6 n \cdot (1 - p) = 240 \cdot (1 - 0.11) = 240 \cdot 0.89 = 213.6 , which is greater than 10.
    3. N=24565 N = 24565 , which is greater than 20⋅240=4800 20 \cdot 240 = 4800 .

NAME THE PROCEDURE

  • The conditions are met to use a one-sample z-test for proportions.

T: TEST STATISTIC

  • The symbol and value of the random variable on this problem are as follows:

    • p^=31240=0.1292 \hat{p} = \frac{31}{240} = 0.1292

  • The formula setup of the test statistic is as follows: z=p^−pp(1−p)n=0.1292−0.110.11⋅(1−0.11)240 z = \frac{\hat{p} - p}{\sqrt{\frac{p(1 - p)}{n}}} = \frac{0.1292 - 0.11}{\sqrt{\frac{0.11 \cdot (1 - 0.11)}{240}}}

  • Final answer for the test statistic from technology:

    • z=0.82 z = 0.82 (rounded to 2 decimal places)

O: OBTAIN THE P-VALUE

  • Report to 4 decimal places:
    • P-value = 0.2061

M: MAKE A DECISION

  • Since the p-value (0.2061) is greater than the significance level (0.09), we fail to reject the null hypothesis.

S: STATE A CONCLUSION

  • There is not significant evidence to conclude that the proportion of left-handed students at this college is higher than the general American population.

This problem has been solved

Similar Questions

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