How to calculate degrees of freedom for a chi-square test?

A sample of 25 observations provides the following statistics:

$$\text { 6. A sample of } 25 \text { observations provides the following statistics: }$$

a. Calculate and interpret the sample correlation coefficient $r_{x y}$.

b. Specify the competing hypotheses in order to determine whether the population correlation coefficient differs from zero

c. Make a conclusion at the $5 \%$ significance level.

Based on meteorological data for the past century, a local TV weather forecaster estimates that the region's average winter snowfall is 23", with a margin of error of

$${\pm}2$$

inches. Assuming he used a 95% confidence interval, how should viewers interpret this news? Comment on each of these statements:

During 95 of the past 100 winters, the region got between 21" and 25" of snow.

If you roll a die 200 times, what is the approximate probability that you will roll fewer than 25 ones, inclusive? (Round your answer to two decimal places.)

If you roll a die 100 times, what is the approximate probability that you will roll between 15 and 20 ones, inclusive? (Round your answer to two decimal places.)

The number of accidents in a production facility has a Poisson distribution with a mean of 2.6 per month.

For a given month what is the probability there will be fewer than 2 accidents?

For a given month what is the probability there will be more than 3 accidents?

The random variable x is normally distributed with mean

$$\mu = 18$$

and standard deviation

$$\sigma = 7.6$$

. Find the value of x that has 88.3% of the distribution's area to its left.

Suppose X is a binomially distributed random variable such that $\mu=2$ and $\sigma^{2}=\frac{3}{2} .$ Find P(X = 2).

If X is a binomially distributed random variable with n=50 and $p=\frac{2}{5}$, find $\sigma^{2}$.

The random variable X has a binomial distribution with n = 10 and p = 0.5. Determine the following probabilities: a. P(X = 5) b. P(X ≤ 2) c. P(X ≥ 9) d. P(3 ≤ X < 5)

Assume a binomial probability distribution with n = 50 and π = .25. Compute the following: a. The mean and standard deviation of the random variable. b. The probability that X is 15 or more. c. The probability that X is 10 or less.

In a small city, the number of automobile accidents occur with a Poisson distribution at an average of three per week. a. Calculate the probability that there are at most 2 accidents occur in any given week. b. What is the probability that there is at least two weeks between any 2 accidents?

Kay Paso, who is $3$ years old, tears the labels of all $10$ of the soup cans on her mother's shelf. Her mother knows that there were $2$ cans of tomato soup and $8$ cans of vegetables. She selects $4$ cans at random.
a. What is the probability that exactly $1$ of the $4$ cans is a tomato?
b. What is the probability that at least $1$ of the $4$ cans is a tomato?
c. What is the probability that none of the $4$ cans is a tomato?
d. What relationship exists between the answers to parts b and c?

When constructing a frequency distribution and histogram, explain how to find:

The relative frequency for a class.