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Let x be a random variable that represents the pH ofarterial plasma (acidity of

ID: 2913602 • Letter: L

Question

Let x be a random variable that represents the pH ofarterial plasma (acidity of the blood). For healthy adults, themean of the x distrbution is = 7.4(Reference Merck Manual) Anew drug for arthritis has been developed. However, it is thoughtthat this drug may change blood pH. A random sanple of 31 patientswith arthritis took the drug for 3 months. Blood tests showed theaverage pH to be _ ˜8.1                                                                                                                                     x with sample standard deviation s = 1.9. Use a 5% levelof signifiance to test the claim that the drug has changed(either way) the mean pH level of the blood. Let x be a random variable that represents the pH ofarterial plasma (acidity of the blood). For healthy adults, themean of the x distrbution is = 7.4(Reference Merck Manual) Anew drug for arthritis has been developed. However, it is thoughtthat this drug may change blood pH. A random sanple of 31 patientswith arthritis took the drug for 3 months. Blood tests showed theaverage pH to be _ ˜8.1                                                                                                                                     x with sample standard deviation s = 1.9. Use a 5% levelof signifiance to test the claim that the drug has changed(either way) the mean pH level of the blood.

Explanation / Answer

Let xbe a random variable that represents the pH of arterial plasma(acidity of the blood). For healthy adults, the mean of the xdistribution is = 7.4(Reference Merck Manual) A new drug forarthritis has been developed. However, it is thought that this drugmay change blood pH. A random sample of 31 patients with arthritistook the drug for 3 months. Blood tests showed the average pH to beX_bar ˜ 8.1 with sample standard deviation s = 1.9. Use a 5%level of significance to test the claim that the drug haschanged (either way) the mean pH level of theblood.

{Null Hypothesis} = {H0: Mean Blood PH With New Drug EQUALS7.4 }
{Alt Hypothesis} = { Ha: MeanBlood PH With New Drug NOT= 7.4 }
{Test Level Of Significance} = 5%

{Population Mean} = = 7.4
{Sample Size} = N = 31
{Degrees Of Freedom} = df = (31) - 1 = 30
{Sample Mean} = (X_bar) = 8.1
{Sample Std Dev} = s = 1.9

{"t" Test Value} = ( (X_bar)- )/(s/Sqrt[N]) =
     = ((8.1)- (7.4))/((1.9)/Sqrt[31])
     = 2.051
{P-Value For "t" Test Value(2.051),2-Tail, df=30 (from tables)} = 0.0491

---->    {Since testP-Value (0.0491) is LESS than (0.05),
              we REJECT Null Hypothesis and acceptAlternate
   Hypothesisthat the new drug causes a significant
              difference in mean blood PH at the 5%Level Of
              Significance.}

             
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