Answer:
CI(99%) = ( 0.93 , 2.07)
Therefore at 99% confidence interval (a,b) = ( 0.93 , 2.07)
Critical value z(at 99% confidence) = z(0.005) = 2.58
Step-by-step explanation:
Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.
The confidence interval of a statistical data can be written as.
x+/-zr/√n
Given that;
Mean gain x = 1.5
Standard deviation r = 0.58
Number of samples n = 7
Confidence interval = 99%
Critical value z(at 99% confidence) = z((1-0.99)/2)
z(0.005) = 2.58
Substituting the values we have;
1.5+/-2.58(0.58/√7)
1.5+/-2.58(0.2192)
1.5+/-0.565536
1.5+/-0.57
= ( 0.93 , 2.07)
Therefore at 99% confidence interval (a,b) = ( 0.93 , 2.07)
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Answer:
The decision rule is
Fail to reject the null hypothesis
The conclusion is
There is no sufficient evidence to show that the designer's claim of a better shoe is supported by the trial results.
Step-by-step explanation:
From the question we are told that
The population mean is 
The sample size is n = 25
The sample mean is 
The standard deviation is 
Let assume the level of significance of this test is 
The null hypothesis is 
The alternative hypothesis is 
Generally the degree of freedom is mathematically represented as

=> 
=> 
Generally the test statistics is mathematically represented as

=> 
=> 
Generally from the student t distribution table the probability of obtaining
to the right of the curve at a degree of freedom of
is

From the value obtained we see that
hence
The decision rule is
Fail to reject the null hypothesis
The conclusion is
There is no sufficient evidence to show that the designer's claim of a better shoe is supported by the trial results.
We are asked to determine the limits of the function cos(2x) / x as x approaches to zero. In this case, we first substitute zero to x resulting to 1/0. A number, any number divided by zero is always equal to infinity, Hence there are no limits to this function.