Question

1.      The effectiveness of a blood-pressure drug is being investigated. An experimenter finds that, on average, the reduction in systolic blood pressure is 47.3 for a sample of size 1066 and standard deviation 6.8. Estimate how much the drug will lower a typical patient's systolic blood pressure (using a 95% confidence level).
Enter your answer as a tri-linear inequality accurate to one decimal place (because the sample statistics are reported accurate to one decimal place).

< μμ <

A shareholders' group is lodging a protest against your company. The shareholders group claimed that the mean tenure for a chief exective office (CEO) was at least 10 years. A survey of 76 companies reported in The Wall Street Journal found a sample mean tenure of 8.4 years for CEOs with a standard deviation of s=s= 4.3 years (The Wall Street Journal, January 2, 2007). You don't know the population standard deviation but can assume it is normally distributed. You want to formulate and test a hypothesis that can be used to challenge the validity of the claim made by the group, at a significance level of α=0.10α=0.10. Your hypotheses are:
      Ho:μ≥10Ho:μ≥10
      Ha:μ<10Ha:μ<10
What is the test statistic for this sample?
test statistic = (Report answer accurate to 3 decimal places.)
What is the p-value for this sample?
p-value = (Report answer accurate to 4 decimal places.)
The p-value is... less than (or equal to) αα greater t

Answer 1

1. The statistical software output for this problem is:

One sample T summary confidence interval:
μ : Mean of population

95% confidence interval results:

Mean	Sample Mean	Std. Err.	DF	L. Limit	U. Limit
μ	47.3	0.20827172	1065	46.89133	47.70867

Hence,

95% confidence interval will be:

46.9 < μ < 47.7

2. The statistical software output for this problem is:

One sample T summary hypothesis test:
μ : Mean of population
H₀ : μ = 10
H_A : μ < 10

Hypothesis test results:

Mean	Sample Mean	Std. Err.	DF	T-Stat	P-value
μ	8.4	0.49324383	75	-3.2438318	0.0009

Hence,

Test statistic = -3.244

p - Value = 0.0009

The p - value is less than (or equal to) α