Question

1. You are working for a drug company that is testing a drug intended to increase heart rate. A sample of 100 randomly treated male patients between 30 and 50 experienced a mean heart beat of 76.5 beats per minute. The population mean for this same demographic group is generally known to be 75 beats per minute, and the standard deviation of heart beat for this group is to 5.6. Before putting the drug up for market, the company wants to make sure the drug is effective — that is, it actually increases heart rates. (80 Points)

(a) Write the research hypothesis that the company wants to show, and the null hypothesis that it wants to disprove. (10 Points)

(b) You know that heart rates are normally distributed, and so you set out to test the hypothesis using a Z-statistic. The company is very risk averse — you don’t want to market an ineffective drug, because you might get sued. What sort of error are you therefore most worried about — type 1 or type 2? Why? (10 Points)

(c) Given this concern, should you choose to test the drug at a 0.05 significance level, or at a 0.001 significance level? That is, should α = 0.05 or α = 0.001? (10 Points)

(d) Calculate and report the Z-statistic. Show your work. (10 Points)

(e) Find the p-value of that Z-statistic in Excel and report it. (10 Points)

(f) Decide whether to reject the null, according to your calculated p-value and your chosen α. Should the company market the drug? Why or why not? (10 Points)

(g) Calculate the 95% confidence interval around the sample mean found by the company. (Recall that 95% of the data in a standard normal distribution are within 1.96 standard deviations of the mean.) Show your work. (10 Points)

(h) How do you interpret this confidence interval? (10 Points)

Answer 1

SOLUTION a: NULL HYPOTHESIS H0: bpm

ALTERNATIVE HYPOTHESIS Ha: bpm

b) Type I ERROR : Rejection of null hypothesis H0 when H0 is true. That is rejecting that hypothesis that drug does not increase bpm and actually it is true.  

c) To reduce Type 1 Error we need to choose small level of significance so I will select α = 0.001.

d) Test statistic is

e) P value= 0.003681108 By using (NORMSDIST(z))

f) Since P value is GREATER than the level of significance therefore DO NOT REJECT NULL HYPOTHESIS H0. No,the company should not  market the drug because it is ineffective.

g) Z critical = 1.96
s_M = √(5.6²/100) = 0.56

μ = M ± Z(s_M)
μ = 76.5 ± 1.96*0.56
μ = 76.5 ± 1.098

95% CI [75.402, 77.598].

h) We can be 95% confident that the population mean (μ) of beats per minute falls between 75.402 and 77.598.