Question Set 1: Internet Usage

Access to high-speed internet is limited in many rural areas in central Pennsylvania. A rural internet company is looking to build towers and expand access to one of these areas. However, in order to justify the expense and start building, at least 85% of the adult residents in the area need to be internet-users.

A research firm working for the company is going to study if the percentage of adult residents in this area who use the internet is greater than 85%.

Question Set 1_1_A

State the null and alternative hypotheses for the scenario above.

H₀: (Hint: The sign for H₀is always =)

H_a: (Hint: The sign for H_ais , or ?)

Question Set 1_2_B

What is the definition of a Type I error?

Question Set 1_2_C

What is the definition of a Type II error?

Question Set 1_3_D

Suppose we compute a p-value and conclude that the population proportion of adult residents in this area who use the internet is greater than 0.85 (i.e. 85%), but in fact it is truly not greater than 0.85.

Is this an example of a Type I error or a Type II error? Explain your answer.

Question Set 1_4_E

The most common alpha level is 0.05. When is a higher alpha level (e.g. 0.10) typically used?

Hint: Seehttps://online.stat.psu.edu/stat200/lesson/6/6.2

Question Set 1_5_F

When is a smaller alpha level (e.g. 0.01) typically used?

Question Set 2_B Compute Cohen's d. For the formula, see https://online.stat.psu.edu/stat200/lesson/6/6.4 => and find the sentence that begins "For a single mean..." Per the hypotheses provided above yo = 53. The sample mean ( x = 57.2) and standard deviation (s = 4.6) are also provided above. Show your work.Question Set 2: Temperature Based on the national weather report, the mean temperature in California is 53 F. However, the Agriculture Weather Services claims that the mean temperature in California is more than 53 F per the farmers' reports. Thus, here are our null and alternative hypotheses: Huz,u,= 53F Ha :,u> 53F In a random sample of 15 farmers, the mean temperature was 512 F with a standard deviation of 4.60 F. A right-tailed hypothesis test was conducted, which resulted in a p-value of 0,002