Question

Nikki wants to make a mobile phone application for her university, which has a student population of 7200 . However, she only has enough time to develop either an Android app or an iOS app. To help her make a decision, she needs to estimate the proportion of Android phone users among the student population (Every student is either an Android phone user or an iPhone user). She randomly selects 35 students from the university records and finds that 21 of them are using Android phones. Construct a 98% confidence interval for the proportion of android phone users among the student population. a. (0.438,0.762) b. (0.407,0.792) c. (0.412,0.945) d. (0.386,0.813) Suppose Nikki wishes to repeat her study at a new university. Which of the following must be true about the confidence interval she will calculate? Select one: a. It must be computed based on a representative sample to be valid b. If it is computed correctly, it should contain the true population parameter c. The sample size needs to be greater than or equal to 30 d. All of the above

Answer 1

The 98% confidence interval for the proportion of Android phone users is (0.407, 0.792). The statement that must be true for the confidence interval at a new university is that it must be based on a representative sample to be valid.

Step-by-step explanation:

To construct a 98% confidence interval for the proportion of Android phone users among the student population, we use the formula:

Confidence interval = p ± Z*sqrt[(p(1-p))/n]

Where p is the sample proportion, Z is the Z-score for the confidence level, and n is the sample size.

Given that 21 out of 35 students in the sample use Android phones, we have:

• Sample proportion (p) = 21/35 = 0.6
• Sample size (n) = 35

The Z-score for a 98% confidence level is approximately 2.33 (from Z-tables).

Plugging these values into the formula:

Error Margin (E) = 2.33 * sqrt[(0.6*(1-0.6))/35]

Confidence interval = 0.6 ± E

After calculations, the correct confidence interval is option b. (0.407, 0.792).

As for the statements about what must be true about the confidence interval Nikki will calculate at a new university:

• 
  
• The confidence interval must be based on a representative sample to be valid
• 
  
• There is no guarantee that a correctly computed confidence interval should contain the true population parameter, although it's designed with that intention
• 
  
• While having a sample size of at least 30 can be a rule of thumb for the Central Limit Theorem to apply, it is not a rigid requirement

Therefore, the correct answer is a. It must be computed based on a representative sample to be valid.