In October 2024
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A study found that 68% of the population owns a home in a random sample of 150 households 92 owned a home at the a=0.01 level is there enough evidence to reject the claim
- A fruit juice franchise company has a policy of opening new fruit juice stand only on those areas that have a mean household income of at least ₱30,500 a month. The company is currently considering an area in which to open a new fruit juice stand. The company’s research department took a sample of 25 households from this area and found that the mean monthly income of these households is ₱32,600. Using 5% significance level, would you conclude that the company should open a fruit juice stand in the area? Also, find the 95% confidence interval of the true mean.
A consumer advocacy group suspects that a local supermarket’s 500 grams of sugar actually weigh less than 500 grams. The group look a random sample of 20 such packages, weigh each one, and found the mean weight for the sample to be 496 grams with standard deviation of 8 grams. Using 1% significance level, would you conclude that the mean weight is less than 500 grams? Also, find the 99% confidence interval of the true mean.
Phone Battery Life. Battery life between charges for a certain mobile phone is 20 hours when the primary use is talk time and drops to 7 hours when the phone is primarily used for Internet applications over a cellular network. Assume that the bat¬tery life in both cases follows an exponential distribution. a. Show the probability density function for battery life for this phone when its primary use is talk time. b. What is the probability that the battery charge for a randomly selected phone will last no more than 15 hours when its primary use is talk time? c. What is the probability that the battery charge for a randomly selected phone will last more than 20 hours when its primary use is talk time? d. What is the probability that the battery charge for a randomly selected phone will last no more than 5 hours when its primary use is Internet applications?
Solve the given problems.
1. A population consists of the four numbers 1, 2, 4 and 5. List all the possible
samples of size n = 2
which can be drawn with replacement from the population.
Find the following:
a. Population mean
b. Population variance
c. Population standard deviation.
d. Mean of the sampling distribution of sample means
e. Variance of the sampling distribution of sample means
f. Standard deviation of the sampling distribution of sample means
Verify the central limit theorem for a random variable X that is binomially
distributed, and thereby establish the validity of the normal approximation to
the binomial distribution.
What is the normal probability distribution for P ( -0.21< z < 0.85)?
Given the population 3 5,7,9,11,13
How many samples can be made from the population with sample size of 3?
Calculate the mean of the sampling distribution
Compute the variance o the sampling distribution
The standard deviation of the number of minutes of calls of a certain subscriber is 40 min per day. A sample of 10 days gave a variance of 38 min. Test the hypothesis with α = 0.05 that the standard deviation of the call usage is not equal to 40.
The mean of the sample means in a sampling distribution is 2.6. What is the mean of the population from which the scores are sampled?
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