The sodium content of a popular sports drink is listed as 205 mg in a 32-oz bottle. Analysis of 20 bottles indicates a sample mean of 219.2 mg with a sample standard deviation of 18.0 mg. (a) State the hypotheses for a two-tailed test of the claimed sodium content. H0: μ ≥ 205 vs. H1: μ < 205 H0: μ ≤ 205 vs. H1: μ > 205 H0: μ = 205 vs. H1: μ ≠ 205

If we compare the p value and a significance level for example we see that so we can conclude that we have enough evidence to reject the null hypothesis, and we can conclude that the lifetime is signficantly different from 205 hours.    

Step-by-step explanation:

Data given and notation    

represent the sample mean

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 (variable of interest)    

represent the p value for the test (variable of interest)    

State the null and alternative hypotheses.    

We need to apply a two tailed  test.  

What are H0 and Ha for this study?    

Null hypothesis:    

Alternative hypothesis :  

Compute the test statistic  

The statistic for this case is given by:  

(1)    

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".    

Calculate the statistic    

We can replace in formula (1) the info given like this:    

Give the appropriate conclusion for the test  

The degreed of freedom are:

Since is a two sided test the p value would be:    

Conclusion    

If we compare the p value and a significance level for example we see that so we can conclude that we have enough evidence to reject the null hypothesis, and we can conclude that the lifetime is signficantly different from 205 hours.    

H0: mu equals 205 vs. H1: mu not equals 205.

Step-by-step explanation:

A null hypothesis (H0) is a statement from a population parameter which is either rejected or accepted (fail to reject) upon testing. It expresses equality.

An alternate hypothesis (H1) is also a statement from the population parameter which negates the null hypothesis and is accepted if the null hypothesis is true. It expresses inequality.

A two-tailed test is one in which the alternate hypothesis is expressed using any of the inequality signs below:

not equal to, less than or equal to, greater than or equal to.

i believe the answer is d.

hope it you! : d

a) one student is chosen from classroom a, then a student is chosen from classroom b.  

step-by-step explanation:

independent events are ones in which the probability of one event does not affect the probability of the second event.

one student is chosen from classroom a; this does not affect the chances of choosing a student from classroom b.   this makes these independent events.

when one card is chosen from a standard deck and then set aside before a second card is chosen, the probability of the second card being chosen changes.   this makes them dependent events.

when one student is chosen from classroom a and then a second student is chosen from classroom a, the probability of choosing the second student changes.   this makes them dependent events.

when a letter is chosen from the alphabet and then a second letter is chosen, the probability of choosing the second letter changes.   this makes them dependent events.