a) According to the U.S. National Weather Service, at any given moment of any day, approximately 1000 thunderstorms are occurring worldwide. Many of these storms include lightning strikes. Sensitive electronic equipment is used to record the number of lightning strikes worldwide every day. 19 days were selected at random, and the number of lightning strikes on each day was recorded. The sample mean was 9.3 million. Assume the distribution of the number of lightning strikes per day is normal and has a population standard deviation of 0.51 million. Please use 4 decimal places for all critical values.

b) Should you use a z distribution or a t distribution in this problem? Note that you will only get one try to get this question correct.

c) Please explain the correct answer.

d) Find the 95.6% confidence interval for the true mean number of lightning strikes per day.

i) If this would be a z distribution, what would be the critical value? Please use 4 decimal places.

ii) If this would be a t distribution, what would be the critical value? Please use 4 decimal places.

iii) If this would be a t distribution, what would be the degrees of freedom?

iv) The 95.6% confidence interval for the true mean number of lightning strikes per day is

e) Interpret your answer from the interval above (part d)

f) Please show all of the code for this part (part d) below.

g) Determine the number of days that need to be sampled to ensure that the half-width of the interval in b) is at most 0.19 million. Assume a confidence level of 95.6% Please use at least 4 decimal places in all numbers used (unless the number is exact). What is the new sample size?

h) Please show all of the code for this part (part g) below

i) In a previous year, the number of measured lightning strikes world wide was 9.11 million. Do you think that the number of lightning strikes has changed from 9.3 million? Please explain your answer

Costello Music Company has been selling electronic organs over the past 5 years. Sales were initially low but have grown over time. Ray Costello, the owner of the company, wants to predict the sales for the upcoming year using the number of sales that Costello Music Company has experienced. The sales totals are given in the following table.

a) Using the centered moving average approach (CMA) what are the seasonal indexes for the four quarters?

b) In which quarter does Costello Music Company experience their largest seasonal effect? Does this result seem reasonable? Explain your answer.

c) Using multiplicative decomposition predict the level of sales for each quarter next year. Report your results.

As part of a study investigating the effects of vigorous exercise on risk of coronary heard disease, researchers measured HDL concentrations (mg/dL) in a sample of 19 male marathon runners as well as in a sample of 32 men who do not regularly exercise. The data are summarized below: Mean St. Dev. Marathon runners 51.3 mg/dL 14.2 mg/dL Do not exercise 44.0 mg/dL 15.0 mg/dL a. Assuming that the two distributions of HDL concentrations are normally distributed with equal variances, run the appropriate test to determine if there is a significant difference between marathon runners and men who don’t exercise. Given: critical = 2.00 and SePooled = 2.43 mg/dl (4pts) b. Name a possible confounding variable in this analysis and what impact it might have on the applicability of the results.

A researcher crossed several randomly-chosen pink tree peonies, Paeonia suffruticosa, to test a genetic model of inheritance. She expected to see red:pink:white offspring colors in the ratio of 12:3:1. Below are the observed color proportions of the 83 plants in the study: Observed Proportions of Progeny Colors Red Pink White 0.747, 0.205, 0.048, Conduct a hypothesis test to determine if the observed proportions significantly differ from the expected ratio. Given: critical = 5.99

5. Your statistics professor is involved in an educational outreach program designed to increase women’s participation in science, technology, engineering, and mathematics (STEM). The two-week educational program involved fieldtrips and activities designed to increase participants’ knowledge toward STEM.

On the first day of the education program, a pre-test is administered to all students. On the final day of the educational program, an identical post-test is administered. After the educational program ends, your professor asks you to help her analyze the results. Your professor predicts that pre- and post-test scores will differ significantly and wants to use an alpha level of 0.01. (50 Points)

1. Are you running a one-tailed or two-tailed test?

2. Write your alternative and null hypotheses.

3. Which statistical analysis will you use to run your test (e.g. one-sampled t-test, an independent-samples t-test, a paired t-test, or chi-square test)?

4. Run your statistical analysis using SPSS. Write your conclusion.

(Remember, if you are running a one-tailed test, your alpha value is located in one-tail, meaning your p-value needs to be less than 0.01 to reject the null hypothesis.

If you are running a two-tailed test, your alpha value is divided in half, meaning your p-value needs to be less than 0.005 to reject the null hypothesis)

Revisit Bryden’s sock drawer from earlier in the test (4 Cool socks, 6 Hunk socks, 2 Genius socks). If Mr. Smith draws out two socks, one at a time for Bryden to wear, what is the probability that they do not match?  

4. [5 marks] Suppose that Best Buy sells 4 TVs per day on average.

a) [1 marks] What is the probability that 8 TVs will be sold in a day?

b) [2 marks] What is the probability that fewer than 3 TVs (inclusive) will be sold in a day?

c) [2 marks] Suppose 5 customers enter Best Buy independently. The probability that a single customer will buy a TV is 0.1. What is the probability that at least one of these 5 customers buys a TV? Do not round your answer.

Find the probability of a correct result by finding the probability of a true positive or a true negative.

ultiplication problems

The following table contains data regarding compliance with following directions on prescriptions with the level of

education a person has. Use this data to answer the following questions.

13. If 2 of the 100 subjects are randomly selected, find the probability that they are both PhD’s who followed the

prescription.

14. If you randomly select two people, what is the probability that you will select a person who has only their high

school diploma and a person who doesn’t follow the prescription?

15. If you randomly select two people, what is the probability that you will select a person who has their master’s

degree and a person who follows the prescription?

16. If you randomly select two people, what is the probability that you will select a person with a PhD who doesn’t

follow their prescription and a person with a Master’s degree who doesn’t follow their prescription?

Find the probability of a false positive (Type I error) or false negative (Type II error).

Let x = age in years of a rural Quebec woman at the time of her first marriage. In the year 1941, the population variance of x was approximately σ² = 5.1. Suppose a recent study of age at first marriage for a random sample of 51 women in rural Quebec gave a sample variance s² = 2.4. Use a 5% level of significance to test the claim that the current variance is less than 5.1. Find a 90% confidence interval for the population variance.(a) What is the level of significance?


State the null and alternate hypotheses.

H_o: σ² = 5.1; H₁: σ² > 5.1H_o: σ² < 5.1; H₁: σ² = 5.1    H_o: σ² = 5.1; H₁: σ² < 5.1H_o: σ² = 5.1; H₁: σ² ≠ 5.1

(b) Find the value of the chi-square statistic for the sample. (Round your answer to two decimal places.)


What are the degrees of freedom?


What assumptions are you making about the original distribution?

We assume a binomial population distribution.We assume a uniform population distribution.    We assume a exponential population distribution.We assume a normal population distribution.

(c) Find or estimate the P-value of the sample test statistic.

P-value > 0.1000.050 < P-value < 0.100    0.025 < P-value < 0.0500.010 < P-value < 0.0250.005 < P-value < 0.010P-value < 0.005

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis?

Since the P-value > α, we fail to reject the null hypothesis.Since the P-value > α, we reject the null hypothesis.    Since the P-value ≤ α, we reject the null hypothesis.Since the P-value ≤ α, we fail to reject the null hypothesis.

(e) Interpret your conclusion in the context of the application.

At the 5% level of significance, there is insufficient evidence to conclude that the variance of age at first marriage is less than 5.1.At the 5% level of significance, there is sufficient evidence to conclude that the that the variance of age at first marriage is less than 5.1.    

(f) Find the requested confidence interval for the population variance. (Round your answers to two decimal places.)

Interpret the results in the context of the application.

We are 90% confident that σ² lies below this interval.We are 90% confident that σ² lies above this interval.    We are 90% confident that σ² lies outside this interval.We are 90% confident that σ² lies within this interval.

We are nt allowed ro use z score, we must use a bell curve to find these.

The age of members of seniors curling club are normally distributed, with mean of 63 years and a standard deviation of 4 years. What percent if the curlers in each of the following age groups?

A) between 55 and 63 years old

PLEASE SHOW ALL WORK, I AM LOST

The probability for a family having x dogs is given by:

Find the expected number of dogs that a family will have. Round to the nearest tenth.

14.4 General Kleinherbst is concerned with the VD (venereal disease) epidemic among soldiers in Europe. At a non-routine inspection of 100 troops, 31 were found to have VD. Kleinherbst requires all troops to view the award-winning film VD: Just between Friends. At another inspection 180 days later, Kleinherbst finds that 43 of the 200 troops inspected have VD. What can you say about the program statistically, managerially, and from a research design point of view?

80. An NHANES report gives data for 654 women aged 20 to 29 years. The mean BMI of these 654 women was 26.8. On the basis of the sample, estimate the mean BMI in the population of all 20.6 million women in the age group. Let us assume that the sample is from a normal population with standard deviation of 7.5.

    1. a) Construct a 95% confidence interval for mean BMI of all women

    2. b) Construct both a 90% and 99% confidence interval for the mean BMI in this population?

    3. c) How does increasing the confidence level change the margin of error of a confidence interval when the

       sample size and population standard deviation remain the same?

    4. d) Suppose that the survey above had a sample size of just 100 women. What is the 95% confidence interval

       for this situation? Is it different from the initial case?

    5. e) Construct a 95% confidence interval for samples with 400 and 1600 women. How are these confidence

       intervals different?