Also Use teachonology to find the P-Value. p-Value=_____ Should you reject or no

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Also

Use teachonology to find the P-Value. p-Value=_____

Should you reject or not reject the null hypothesis. If p-value is > or < than (X

In February 2008, an organization surveyed 1040 adults aged 18 and older and found that 534 believed they would not have enough money to live comfortably in retirement. Does the sample evidence suggest that a majority of adults in a certain country believe they will not have enough money in retirement? Use the =0.1 level of significance What are the null and alternative hypotheses? Ho : pl | I-J versus H 1 :

Explanation / Answer

For this case, the Null hypothesis is that a majority of adults will NOT have enough money in retirement.

The Alternate hypothesis is that a majority of adults will have enough money in retirement.

For a discrete binomial variable, value for each individual could be 0 or 1. If the sample size is N, the Binomial probability distribution gives the likelihoods of N+1 cases (no one has value 1, only 1 individual has value 1, 2 individuals have value 1, and so on.)

Now, we can use the Binomial distribution function to calculate the level (number of 1s - NOT have enough money) above which, the Null hypothesis cannot be rejected.

For alpha = 0.1, binomial distribution critical value is calculated using BINOM.INV() in Excel (Windows) or CRITBINOM(Ntotal, probability_to_test, alpha) function in Numbers (Mac).

For the given test, Ntotal = 1040, alpha = 0.1 (significance level) and probability to test = 1/2 (majority means more than half the population)

Critical value = 499. As we got 534 True values, which is greater than 499 - the critical value - we can say that we can NOT reject the Null hypothesis.

p-value = 1-BINOM.DIST(Nsuccess,Ntotal,probability_to_test,TRUE)

p-value = 0.184263 (Answer)

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