Excel's function can be used to calculate a p-value for a hypothesis test when σ is unknown. a. rand b. t. dist c. norm. s.dist d. not enough information is given to answer this question.

b. T.DIST

Step-by-step explanation:

Previous concepts

The t distribution (Student’s t-distribution) is a "probability distribution that is used to estimate population parameters when the sample size is small (n<30) or when the population variance is unknown".

The shape of the t distribution is determined by its degrees of freedom and when the degrees of freedom increase the t distirbution becomes a normal distribution approximately.  

The degrees of freedom represent "the number of independent observations in a set of data. For example if we estimate a mean score from a single sample, the number of independent observations would be equal to the sample size minus one."

Solution to the problem

a. RAND

False, since this function is to generate a random number between 0 and 1. And is not used to calculate p values

b. T.DIST

Correct, since th population deviation is unknown and if we find the degrees of freedom we can calculate the p value with this function.

c. NORM.S.DIST

False, because this is in order to calculate the p value when the population deviation is given

d. Not enough information is given to answer this question.

False we have enough info to conclude this.

b. T.DIST

Step-by-step explanation:

Excel's T.DIST function is used to calculate the p-value for a hypothesis test when the standard deviation is unknown. It makes use of Student's T distribution with single tail. It is generally used when the data set size is relatively small making it difficult to compute the standard deviation of the population. The function facilitates hypothesis testing in such scenarios.

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation: