Answer:
The degrees of freedom are given by:
the p value for this case would be given by:
For this case we see that the p value is higher than the significance level so then we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly different from 2564 mm
Step-by-step explanation:
Information given
represent the mean height for the sample
represent the sample standard deviation
sample size
represent the value that we want to test
represent the significance level for the hypothesis test.
t would represent the statistic
represent the p value
Hypothesis to test
We want to check if the true mean is equal to 2564 mm, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
The statistic is given by:
(1)
Replacing we got:
The degrees of freedom are given by:
the p value for this case would be given by:
For this case we see that the p value is higher than the significance level so then we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly different from 2564 mm
Answer:
Binomial distribution requires all of the following to be satisfied:
1. size of experiment (N=27) is known.
2. each trial of experiment is Bernoulli trial (i.e. either fail or pass)
3. probability (p=0.14) remains constant through trials.
4. trials are independent, and random.
Binomial distribution can be used as a close approximation, with the usual assumption that a sample of 27 in thousands of stock is representative of the population., and is given by the probability of x successes (defective).
P(x)=C(N,x)*p^x*(1-p)^(n-x)
where N=27, p=0.14, and C(N,x) is the number of combinations of x items out of N.
So we need the probability of <em>at most one defective</em>, which is
P(0)+P(1)
= C(27,0)*0.14^0*(0.86)^(27) + C(27,1)*0.14^1*(0.86^26)
=1*1*0.0170 + 27*0.14*0.0198
=0.0170+0.0749
=0.0919
Answer: 4+2=6
____________
Assuming by "20111" you mean 2011.
The difference in years is 2011 and 1990 is 21 years.
In 21 years the rate of change was "-$1850" (44,450 - 6,300).
Furthermore, this can be divided by 21 to get the AVERAGE rate of change in 1 year
21 years / -1850 = -$88.096 (3 DP)