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The table below contains pulse rates after running for 1 minute, collected from a sample of females who drink alcohol. The mean pulse rate after running for 1 minute of females who do not drink is 97 beats per minute. Do the data show that the mean pulse rate of females who do drink alcohol is higher than the mean pulse rate of females who do not drink? Test at the 2% level.pulse rate after running one minute in bpm57124122110801107998667080124649780701094185621189575140107671313796131159421141079896P: 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: bpm 𝐻𝐴: bpm A:  Assumptions     Since information was collected from each object, what conditions do we need to check?     Check all that apply.    outliers in the data𝑛≥30 or normal population𝑁≥20𝑛𝑛(𝑝̂)≥10σσ is unknownσσ is known𝑛𝑝≥10𝑛(1-𝑝)≥10no outliers in the data𝑛(1-𝑝̂)≥10     Check those assumptions:     1. Is the value of 𝜎 known?      2. Which of the following is the correct modified boxplot?         20406080100120140160pulse rate after running one minute in bpm377096135.5159[Graphs generated by this script: setBorder(15); initPicture(20,160,-3,6);axes(20,100,1,null,null,1,'off');text([81,-3],"pulse rate after running one minute in bpm");line([37,2],[37,4]); rect([70,2],[135.5,4]); line([96,2],[96,4]);line([159,2],[159,4]); line([37,3],[70,3]); line([135.5,3],[159,3]);fontsize*=.8;fontfill='blue';text([37,4],'37','above');text([70,4],'70','above');text([96,4],'96','above');text([135.5,4],'135.5','above');text([159,4],'159','above');fontfill='black';fontsize*=1.25;]20406080100120140160pulse rate after running one minute in bpm377096112159[Graphs generated by this script: setBorder(15); initPicture(20,160,-3,6);axes(20,100,1,null,null,1,'off');text([81,-3],"pulse rate after running one minute in bpm");line([37,2],[37,4]); rect([70,2],[112,4]); line([96,2],[96,4]);line([159,2],[159,4]); line([37,3],[70,3]); line([112,3],[159,3]);fontsize*=.8;fontfill='blue';text([37,4],'37','above');text([70,4],'70','above');text([96,4],'96','above');text([112,4],'112','above');text([159,4],'159','above');fontfill='black';fontsize*=1.25;]20406080100120140160pulse rate after running one minute in bpm377083112159[Graphs generated by this script: setBorder(15); initPicture(20,160,-3,6);axes(20,100,1,null,null,1,'off');text([81,-3],"pulse rate after running one minute in bpm");line([37,2],[37,4]); rect([70,2],[112,4]); line([83,2],[83,4]);line([159,2],[159,4]); line([37,3],[70,3]); line([112,3],[159,3]);fontsize*=.8;fontfill='blue';text([37,4],'37','above');text([70,4],'70','above');text([83,4],'83','above');text([112,4],'112','above');text([159,4],'159','above');fontfill='black';fontsize*=1.25;]20406080100120140160pulse rate after running one minute in bpm3753.596112159[Graphs generated by this script: setBorder(15); initPicture(20,160,-3,6);axes(20,100,1,null,null,1,'off');text([81,-3],"pulse rate after running one minute in bpm");line([37,2],[37,4]); rect([53.5,2],[112,4]); line([96,2],[96,4]);line([159,2],[159,4]); line([37,3],[53.5,3]); line([112,3],[159,3]);fontsize*=.8;fontfill='blue';text([37,4],'37','above');text([53.5,4],'53.5','above');text([96,4],'96','above');text([112,4],'112','above');text([159,4],'159','above');fontfill='black';fontsize*=1.25;]          Are there any outliers?      3. 𝑛 = which is           Is it reasonable to assume the population is normally distributed?  N: Name the test     The conditions are met to use a .T: Test Statistic     The symbol and value of the random variable on this problem are as follows:     = bpm     The test statistic formula set up with numbers is as follows:     Round values to 2 decimal places. 𝑡=𝑋¯-𝜇𝑠𝑛=(( - ) / / ))      The final answer for the test statistic from technology is as follows:     Round to 2 decimal places.     t = O: Obtain the P-value     Report the final answer 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 conclustion     There significant evidence to conclude bpm

Question

The table below contains pulse rates after running for 1 minute, collected from a sample of females who drink alcohol. The mean pulse rate after running for 1 minute of females who do not drink is 97 beats per minute. Do the data show that the mean pulse rate of females who do drink alcohol is higher than the mean pulse rate of females who do not drink? Test at the 2% level.pulse rate after running one minute in bpm57124122110801107998667080124649780701094185621189575140107671313796131159421141079896P: 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: bpm 𝐻𝐴: bpm A:  Assumptions     Since information was collected from each object, what conditions do we need to check?     Check all that apply.    outliers in the data𝑛≥30 or normal population𝑁≥20𝑛𝑛(𝑝̂)≥10σσ is unknownσσ is known𝑛𝑝≥10𝑛(1-𝑝)≥10no outliers in the data𝑛(1-𝑝̂)≥10     Check those assumptions:     1. Is the value of 𝜎 known?      2. Which of the following is the correct modified boxplot?         20406080100120140160pulse rate after running one minute in bpm377096135.5159[Graphs generated by this script: setBorder(15); initPicture(20,160,-3,6);axes(20,100,1,null,null,1,'off');text([81,-3],"pulse rate after running one minute in bpm");line([37,2],[37,4]); rect([70,2],[135.5,4]); line([96,2],[96,4]);line([159,2],[159,4]); line([37,3],[70,3]); line([135.5,3],[159,3]);fontsize*=.8;fontfill='blue';text([37,4],'37','above');text([70,4],'70','above');text([96,4],'96','above');text([135.5,4],'135.5','above');text([159,4],'159','above');fontfill='black';fontsize*=1.25;]20406080100120140160pulse rate after running one minute in bpm377096112159[Graphs generated by this script: setBorder(15); initPicture(20,160,-3,6);axes(20,100,1,null,null,1,'off');text([81,-3],"pulse rate after running one minute in bpm");line([37,2],[37,4]); rect([70,2],[112,4]); line([96,2],[96,4]);line([159,2],[159,4]); line([37,3],[70,3]); line([112,3],[159,3]);fontsize*=.8;fontfill='blue';text([37,4],'37','above');text([70,4],'70','above');text([96,4],'96','above');text([112,4],'112','above');text([159,4],'159','above');fontfill='black';fontsize*=1.25;]20406080100120140160pulse rate after running one minute in bpm377083112159[Graphs generated by this script: setBorder(15); initPicture(20,160,-3,6);axes(20,100,1,null,null,1,'off');text([81,-3],"pulse rate after running one minute in bpm");line([37,2],[37,4]); rect([70,2],[112,4]); line([83,2],[83,4]);line([159,2],[159,4]); line([37,3],[70,3]); line([112,3],[159,3]);fontsize*=.8;fontfill='blue';text([37,4],'37','above');text([70,4],'70','above');text([83,4],'83','above');text([112,4],'112','above');text([159,4],'159','above');fontfill='black';fontsize*=1.25;]20406080100120140160pulse rate after running one minute in bpm3753.596112159[Graphs generated by this script: setBorder(15); initPicture(20,160,-3,6);axes(20,100,1,null,null,1,'off');text([81,-3],"pulse rate after running one minute in bpm");line([37,2],[37,4]); rect([53.5,2],[112,4]); line([96,2],[96,4]);line([159,2],[159,4]); line([37,3],[53.5,3]); line([112,3],[159,3]);fontsize*=.8;fontfill='blue';text([37,4],'37','above');text([53.5,4],'53.5','above');text([96,4],'96','above');text([112,4],'112','above');text([159,4],'159','above');fontfill='black';fontsize*=1.25;]          Are there any outliers?      3. 𝑛 = which is           Is it reasonable to assume the population is normally distributed?  N: Name the test     The conditions are met to use a .T: Test Statistic     The symbol and value of the random variable on this problem are as follows:     = bpm     The test statistic formula set up with numbers is as follows:     Round values to 2 decimal places. 𝑡=𝑋¯-𝜇𝑠𝑛=(( - ) / / ))      The final answer for the test statistic from technology is as follows:     Round to 2 decimal places.     t = O: Obtain the P-value     Report the final answer 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 conclustion     There significant evidence to conclude bpm

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Solution

P: Parameter

  • What is the correct parameter symbol for this problem?
    • μ\mu
  • What is the wording of the parameter in the context of this problem?
    • The mean pulse rate after running for 1 minute of females who drink alcohol.

H: Hypotheses

  • Fill in the correct null and alternative hypotheses:
    • H0:μ=97H_0: \mu = 97 bpm
    • HA:μ>97H_A: \mu > 97 bpm

A: Assumptions

  • Since information was collected from each object, what conditions do we need to check?

    • n30n \geq 30 or normal population
    • σ\sigma is unknown
    • no outliers in the data
  • Check those assumptions:

    1. Is the value of σ\sigma known?
      • No, σ\sigma is unknown.
    2. Which of the following is the correct modified boxplot?
      • The correct modified boxplot is the one with the following values:
        20 40 60 80 100 120 140 160
        pulse rate after running one minute in bpm
        37 70 96 135.5 159
        
  • Are there any outliers?

    • Yes, there are outliers.
  • n=30n = 30 which is reasonable to assume the population is normally distributed.

N: Name the test

  • The conditions are met to use a one-sample t-test.

T: Test Statistic

  • The symbol and value of the random variable on this problem are as follows:
    • Xˉ=97\bar{X} = 97 bpm
  • The test statistic formula set up with numbers is as follows:
    • t=Xˉμs/n=(9797)s/30t = \frac{\bar{X} - \mu}{s / \sqrt{n}} = \frac{(97 - 97)}{s / \sqrt{30}}
  • The final answer for the test statistic from technology is as follows:
    • t=0.00t = 0.00

O: Obtain the P-value

  • Report the final answer to 4 decimal places.
    • P-value = 0.5000

M: Make a decision

  • Since the p-value 0.5000>0.020.5000 > 0.02, we fail to reject the null hypothesis.

S: State a conclusion

  • There is not significant evidence to conclude that the mean pulse rate of females who drink alcohol is higher than 97 bpm.

This problem has been solved

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