Question

Think of a problem that you may be interested in that deals with a comparison of two population means. Propose either a confidence interval or a hypothesis test question that compares these two means. Gather appropriate data and post your problem (without a solution) in the discussion topic. Later, respond to your own post with the solution for others to check their work. For example, you may want to know if the average weight of a rippled potato chip is the same as the average weight of a non-rippled potato chip. You may weigh rippled regular potato chips fro m a large bag and find weights of 1.7,1.9,2.4,1.3, 1.7, and 2.0 grams. You may weigh non-rippled potato chips from another larg bag and find weights of 1.8, 1.6,1.9, 1.9, and 1.4 grams. Assume a random sample was drawn. Think of a problem that you may be interested in that deals with a comparison of two population proportions. Propose either a confidence interval or a hypothesis test question that compares these two proportions. Gather appropriate data and post your problem (without a solution) in the discussion topic. Later, respond to your own post with your own solution. For example, you may believe that the proportion of adults in California who are vegetarians is more than the proportion of adults in New Hampshire who are vegetarians. In two independent polls, you may find that 109 out of 380 California residents are vegetarians and 39 out of 205 New Hampshire residents are vegetarians. For your response to a classmate (two responses required, one in each option), solve your classmate's confidence interval or hypothesis test problem, using a significance level not previously used Make sure that you use appropriate terminology and specify whether you are using the classical method or the p-value method.

Answer 1

Responds to my friend

Decision rule

Fail to reject the null hypothesis

Conclusion

There is no sufficient evidence to conclude that the proportion of residents in California who are vegetarians is higher than the proportion in New Hampshire who are vegetarian

Explanation:

Here we are going to consider this question

For example, you may believe that the proportion of adults in California who are vegetarians is more than the proportion of adults in New Hampshire who are vegetarians. In two independent polls, you may find that 109 out of 380 California residents are vegetarians and 39 out of 205 New Hampshire residents are vegetarians.

Here we are going to be solving the hypothesis test problem and we will be making use of the p-value method

From the question the we are told that

The first sample size is
`n_1 = 380`

The second sample size is
`n_2 = 205`

The number of California residents that are vegetarian is
`k = 109`

The number of New Hampshire resident that are veterinarian is
`u = 39`

Generally the sample proportion for California residents is

`\^ p_1 = (k)/(n_1)`

=>
`\^ p_1 =(109)/(380)`

=>
`\^ p_1 =  0.2868`

Generally the sample proportion for New Hampshire residents is

`\^ p_2 = (39)/(205)`

=>
`\^ p_2 = 0.1902`

The null hypothesis is
`H_o  :  p_1 -p_2 = 0`

The alternative hypothesis is
`H_a :  p_1 -p_2 > 0`

Generally the test statistics is mathematically represented as

`t  =  \frac{(\^ p_1 - \^ p_2 ) -0}{\sqrt{ (\^ p_1 (1-\^p_1 ))/(n_1)  + (\^ p_2 (1- \^p_2))/(n_2) } }`

=>
`t  =  \frac{( 0.2868 - 0.1902) -0}{\sqrt{ (0.2868 (1-0.2868 ))/(380)  + (0.1902(1- 0.1902))/(205) } }`

=>
`t  =  0.036`

Generally the degree of freedom is mathematically represented as

`df  =  n_1 + n_2 -2`

=>
`df  =  380 + 205 -2`

=>
`df  =  583/tex] </p><p>Generally the probability of  [tex]t  =  0.036` at a degree of freedom of
`df  =  583/tex]  from the t- distribution table is  </p><p>       [tex]p-value  =  P(t >  0.036) =  0.48564732`

Let take the level of significance to be
`\alpha = 0.05`

So from the values obtained we see that
`p-value  >  \alpha` hence the decision rule is

Fail to reject the null hypothesis

The conclusion is

There is no sufficient evidence to conclude that the proportion of residents in California who are vegetarians is higher than the proportion in New Hampshire who are vegetarian