Let x bearandom variable that represents red blood cell caunt C) inmons of cels per cubic milimeter of whole blood. Then x han a datributen that a appreimately normal. For the populaton of healthy female adut, uppose the mean of the dtribution is about 44. Suppen that a 10 De the gven ata ncate tha e populatn mean ac cou Whatelevel of sgancet Rate he andeme butetheses O 4 44 O M () what sampling distriton wi yo Ean the ronale for your hoioe of samoling dron O The standard nomal, inor weaume thatha a nomal distritution and eunknown. The Studenrs urcewe ame tatasanoma auvun ande own O The Studentst e e me thathas anomal dtribution and uninown O The sandard noma, noe weame thathas anomal dton and onon

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Let x be a random variable that represents red blood cell count (RBC) in millions of cells per cubic millimeter of whole blood. Then x has a distribution that is approximately normal, For the population of healthy female adults, suppose the mean of the x distribution is about 4.64, Suppose that a female patient has taken six laboratory blod tests over the past several months and that the RBC count data sent to the patient's doctor are as follows.
4.9 4.2 4.5 4.1 4.4 4.3
() Use a calculator with sample mean and standard deviation keys to find x and s. (Round your answers to two decimal places.)
C) Do the given data indicate that the pooulation mean RBC count for this patient is lower than 4.647 Use a- 0.05.
(a) What is the level of significance?
State the nul and alternate hypotheses.
O Hn: 4- 4.64; H: < 4.64
O Hg: 4 < 4.64; H: H- 4.64
O Hg: u- 4.64; H: H> 4.64
O Ho: H> 4.64; H:u- 4.64
O Hn: H- 4.64; H: H 4.64
(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.
O The standard normal, since we assume that x has a normal distribution and g is unknown.
O The Student's t, since we assume that x has a nomal distribution and o is known.
O The Student's t, since we assume that x has a nomal distribution and o is unknown.
O The standard normal, since we assume that x has a normal distribution and a is known.
What is the value of the sample test statistic? (Round vour answer to three decimal places.)
(c) Estimate the P-value.
O P-value > 0.250
O D.125 < Prvalue < 0..250
O D.050 < Pvalue < 0.125
O D.025 < P-value < 0.050
O D.005 < Pvalue < 0.025
O P-value < 0.005
Sketch the sampling distribution and show the area corresponding to the P-value.
(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level ?
O At the a - 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.
O At the a - 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.
O At the a - 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.
O At the a - 0.05 level, we fail to reject the null hypothesis and conclude the data are r
statistically significant.
(e) Interpret your condusion in the context of the application.
O There is sufficient evidence at the 0.05 level to condude that the population mean RBC count for the patient is lower than 4.64.
O There is insufficient evidence at the D.05 level to condude that the population mean RBC count for the patient is lower than 4.64.
Transcribed Image Text:Let x be a random variable that represents red blood cell count (RBC) in millions of cells per cubic millimeter of whole blood. Then x has a distribution that is approximately normal, For the population of healthy female adults, suppose the mean of the x distribution is about 4.64, Suppose that a female patient has taken six laboratory blod tests over the past several months and that the RBC count data sent to the patient's doctor are as follows. 4.9 4.2 4.5 4.1 4.4 4.3 () Use a calculator with sample mean and standard deviation keys to find x and s. (Round your answers to two decimal places.) C) Do the given data indicate that the pooulation mean RBC count for this patient is lower than 4.647 Use a- 0.05. (a) What is the level of significance? State the nul and alternate hypotheses. O Hn: 4- 4.64; H: < 4.64 O Hg: 4 < 4.64; H: H- 4.64 O Hg: u- 4.64; H: H> 4.64 O Ho: H> 4.64; H:u- 4.64 O Hn: H- 4.64; H: H 4.64 (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. O The standard normal, since we assume that x has a normal distribution and g is unknown. O The Student's t, since we assume that x has a nomal distribution and o is known. O The Student's t, since we assume that x has a nomal distribution and o is unknown. O The standard normal, since we assume that x has a normal distribution and a is known. What is the value of the sample test statistic? (Round vour answer to three decimal places.) (c) Estimate the P-value. O P-value > 0.250 O D.125 < Prvalue < 0..250 O D.050 < Pvalue < 0.125 O D.025 < P-value < 0.050 O D.005 < Pvalue < 0.025 O P-value < 0.005 Sketch the sampling distribution and show the area corresponding to the P-value. (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level ? O At the a - 0.05 level, we reject the null hypothesis and conclude the data are statistically significant. O At the a - 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. O At the a - 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant. O At the a - 0.05 level, we fail to reject the null hypothesis and conclude the data are r statistically significant. (e) Interpret your condusion in the context of the application. O There is sufficient evidence at the 0.05 level to condude that the population mean RBC count for the patient is lower than 4.64. O There is insufficient evidence at the D.05 level to condude that the population mean RBC count for the patient is lower than 4.64.
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