Statistics and Probability Answers

A melting point test of n=10 samples of a binder used in manufacturing a rocket propellant resulted in x =154:2°F. Assume that the melting point is normally distributed with Q=1:5°F: Suppose you want to test the claim that the temperature is different from 155°F: Test the hypothesis at a=0:05: Write down the hypothesis to be tested and show all the steps and calculations.

A melting point test of n D 10 samples of a binder used in manufacturing a rocket propellant resulted in x D 154:2 F. Assume that the melting point is normally distributed with D 1:5 F: Suppose you want to test the claim that the temperature is different from 155 F: Test the hypothesis at D 0:05:

Write down the hypothesis to be tested and show all the steps and calculations.

A new bus route has been established between downtown Pretoria North and Montana. Pandu has taken the bus to work for many years. For the old bus route, she knows from long experience that the mean waiting time between buses at her stop was 20 minutes. However, a random sample of five waiting times between buses using the new route had a mean of 15:1 minutes with sample standard deviation of 6:2 minutes. Does this indicate that the population mean waiting time for the new route is shorter than what it used to be? Test the hypothesis using D 0:05. Assume that X; the waiting time is normally distributed. Write down the hypothesis to be tested and show all the steps and calculations.

A random sample of 16 values of x, obtained from a N(u, Q²)distribution, had a sample mean of 4:2 and a sample variance of 3: Find the 95% confidence interval for u

A.Describe the population of interest.

B.Formulate the appropriate null and alternative hypotheses.

C.Choose the significance level a.

D.Identify if it is two-tailed or one-tailed.

E.Get the critical values from the test statistic table.

F.Sketch the critical regions.

G.Compute for the test-statistic value for population proportion.

H.Find the p-value corresponding to -1.77.

I.Decision Rule.

J.Conclusion.

1. The principal claims that 6 of every 10 learners have access to internet and social networking sites.Upon verification,only 40 out of 70 learners have access to internet and social networking site.At 95% confidence,is the claim true?

2. The health worker claims that less than 30% of COVID-19 cases are asymptomatic.Upon looking at 100 cases,it was found out that 19 of which are asymptomatic.At 99% confidence level,is the claim true?

 The American Automobile Association reports that the average time it takes to respond to an emergency call is 25 minutes. Assume the variable is approximately normally distributed and the standard deviation is 4.5 minutes. If 80 calls are randomly selected, approximately how many will be responded to in less than 15 minutes? 

The lifetime T in tens of hours of a battery has a cumulative distribution function

F(t)={0,t<1

{k(t²+2t-3),1<t<or equal to 1.5

{1,t>5

Find k and hence find p(T>1.2) and find the median of T

The pdf of a random variable x is given by

f(x)={3/2x²,-1<y<1 both inclusive

{0,elsewhere

Find the pdf of y=(1/2)x². Hence state the mean and standard deviation of y

According to German bureau of statistics, the probability of a randomly selected 90 year old German male surviving at least another year is approximately 0.82. if a sample of 20 90 year old German males is chosen what is the probability that

1. 18
2. at least 18
3. at most 18 will survive for at least another year?

Given the first 4 central moments of a random variable x are 0,0.566,0.393 and 0.756 respectively, find the moment coefficient of skewness and kurtosis and interpret them.