STAT作业代写 STAT 200  Written Assignemnt

STAT 200 – Written Assignemnt 2

STAT作业代写 We calculate confidence intervals for the mean because we are trying to learn about plausible values for the sample mean x…

Exercise 1 – Conceptual understanding

Exercise 1.1 – True or False

We calculate confidence intervals for the mean because we are trying to learn about plausible values for the sample mean x

Exercise 1.2 – Select all that apply. STAT作业代写

When calculating a confidence interval for the mean of a population with a known standard deviation, which of the following quantities affects the interval’s width? Select all that apply.

• populationmean: u
• samplemean:
• populationstandard deviation:
• sample standard deviation
• sample size:n
• confidencelevel

Exercise 1.3

For each item selected in Exercise 1.2, explain how it affects the confidence intervals. What happens when the quantity in questions is increased/decreased?

Exercise 1.4 STAT作业代写

Suppose two different samples of the same size, n, are taken from a population. Let us call them samples A and B.

• Case1: If  is known, then the confidence interval for the mean using samples A and B

would have:

• the same
• the same
• the samecenter and
• None of the

• Case2: If is unknown, then the confidence interval for the mean using samples A and B would have: STAT作业代写

• the same
• the same
• the samecenter and
• None of the

• Case3: The confidence interval for the proportion using samples A and Bwould have:
  • the same
  • the same
  • the samecenter and
  • None of the

Exercise 1.5 – True or False:

When estimating the proportion, P, we never know the standard deviation of the population.

Exercise 2 STAT作业代写

One of our new STAT 200 friends is getting married, and guess what? They are inviting all of us to the party! Yay!! Here is the problem, with the pandemic, the mail delivery is getting delayed quite a bit. The courier says that it takes an average of 20 days with a standard deviation of 4 days for a mail to get delivered and that correspondences’ delivery time is independent of each other. Our friends are rushing to get the invitation ready to send to all of their guests. Suppose the wedding date is set to be on May 20th.

• What isthe latest day they should send the invitation to a given guest, so the guest receives the invitation on time (by on time, we mean at least seven days before the wedding) with 90% probability?
• Theyforgot to send an invitation to one of the guests and ended up sending it only on May 6th. What is the probability that the guest will receive the invitation before the wedding (i.e., in 13 days or less)?
• There are 20 people involved in the wedding, among their parents, best people, a friendwho will be officiating, and  They need to prioritize the invitation of these guests, so their presence is “almost” guaranteed. Assuming they are sending the invitations for all these guests on the same day, what is the latest day they should send the invitation, so all the 20 guests receive them at least seven days before the wedding with a 95% probability. STAT作业代写

• What is the probability that the average time of invitations sent to the 20 people involvedin the wedding will be lower than 19 days? List the assumptions you are making.

• Theywant to send all the invitations to their STAT 200 friends  However, the postal service office closes in 4 hours and 30 minutes. Assuming they spend an average of 1 minute to prepare each invitation, with a standard deviation of 10 seconds, what is the probability they finish all the 311 STAT 200’s invitations on time? (Hint: think in terms of the mean.)

• Suppose they will send all the 700 invitations on April 20th. What is the probability thatmore than 80% of their guests receive the invitation at least seven days before the wedding? STAT作业代写
• Ifthey want all the 700 guests to receive their invitations at least ten days before the wedding, with 90% probability, what is the latest day they can send the invitations?
• Supposethat guests who receive the invitation at least seven days before the wedding have a 90% probability of attending the wedding. In comparison, guests who receive the invitation within seven days of the wedding have a 75% probability of attending the wedding. Let N be the number of people that will attend to the wedding. Can we say that N follows a binomial distribution? Explain.

Exercise 3 – Real Data STAT作业代写

In 1987, Indonesia did a national survey to study the use of contraceptives. They sampled married women who were not pregnant. Below is the table of the data collected.

• Obtainthe 95% confidence interval for the proportion of married Indonesian women with a low level of education that use contraceptive methods.
• Whatare the required assumptions/conditions to construct the confidence interval in part (a)?

• Providean interpretation for the confidence

• If the Indonesian Government wanted to conduct a similar survey this year, but this timethey want the sample proportion of married Indonesian women with a low level of education that use contraceptive methods to be within 1% of the true proportion, what sample size would you recommend? STAT作业代写
• The press, at the time, claimed that the majority of women in Indonesia used contraceptives,no matter the education  In other words, the press was claiming that the majority of both, lowly and highly educated Indonesian women, were using contraceptives. Are you able to reject the press’ claim with 99% confidence?
  1. Identifythe population of interest
  2. Statethe null and alternative hypotheses (in words).
  3. Statethe Type I and II errors in the context of the
  4. Listand check any required assumptions/conditions to conduct the hypothesis
  5. Computethe test
  6. Obtainthe p-value and state your conclusion in the context of the  Provide a sketch of your model, shade and label the relevant areas.
  7. Basedon your conclusion in the previous item, what error are you in a position of committing?

Exercise 4 – Real Data STAT作业代写

In this exercise, we will examine two different varieties of wheat seeds: (1) Kama; and (2) Canadian. We are interested in the length of the wheat kernel. We are going to use real data, available here. Below are the samples, of size 30, of kernel length for each wheat variety.

• Kama:

• Canadian: STAT作业代写

• Findthe average kernel length of each type of  Based on these averages alone, can we claim that we know that Kama seeds have a longer true kernel average than Canadian seeds? Briefly explain in 1 – 4 sentences why or why not.
• Next,check how much the kernels’ lengths vary – obtain the standard deviation for each type of wheat.
• Find the standard error ofthe sample averages of each wheat
• Obtain7% confidence intervals for the population mean length of each wheat type.
• Obtaina 95% confidence interval for the difference in true mean lengths between the two wheat types. Provide an interpretation for the confidence interval you obtained. STAT作业代写
• Basedon the interval you obtained in part (e), do the data suggest the true mean seed length is different for the two types of wheat? State your hypotheses (in words or define your notation) and conclusion in the context of the question.

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