Using the data below find the linear correlation coefficient.

x              y               xy               x²               y²

3              4               12              9                 16

4             6                24              16               36

5             7               35              25               49

7            12              84              49               144

8            14              112             64               196

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27           43              267           163              441

Also, utilizing the above data, find the slope and intercept.

Which of the following is not a property of a binomial experiment?

Question 15 options:

Question 16

The probability distribution for the number of goals the Norse soccer team makes per game is given below;

Number of Goals Probability

0 0.05

1 0.15

2 0.35

3 0.30

4 0.15

Refer to the probabilities, what is the probability that in a given game the Norse will score 2 goals or more?

Question 16 options:

A uniform probability distribution is a continuous probability distribution where the probability that the random variable assumes a value in any interval of equal length is

Question 20 options:

1. Suppose the lifespan of a particular bran of calculator battery, X, is approximately normally distributed with a mean of 75 hours and a standard deviation of 10 hours. Please answer A-C

(a) Let x̄ be the mean lifespan of a sample of n batteries. Does x̄ follow a normal distribution? Explain

(b) What is the probability that a single randomly selected battery from the population will have a lifespan between 70 and 80 hours?

(c) What is the probability that 16 randomly selected batteries from the population will have a mean lifespan between 70 and 80 hours?

1. All Clear Windows makes windows for use in homes and commercial buildings. The standards for glass thickness call for the glass to average 0.375 inches with a standard deviation of 0.050 inches. Let x̄ represent the mean thickness of 50 randomly selected windows. Please answer A-C

(a) Can we use a normal distribution to calculate probabilities of x̄? Explain

(b) Describe the mean (center) and standard error (spread) of the sampling distribution of x̄.

(c) Suppose a random sample of n = 50 windows yields a mean thickness of 0.392 inches. What is the likelihood of observing a sample with a mean thickness at least as thick as ours? (In other words, what is the probability that x̄ is greater than 0.392 inches?)

With the above data, could you please help me answer questions 10-13:

Calculate a 95% confidence interval for the mean mileage of make 2. Use the method for single means when σ is not known, but use the Error Mean Square as the estimate of the variance. The degrees of freedom will be the Error DF, not n-1!

Reminders: Confidence Interval = mean ± margin of error Margin of error = critical value * standard error Use critical value for T at α/2 = 0.025 and df = error df (t table or EXCEL T.INV function) Use standard error = √(error mean square/number of observations of that make of car)

10. What was the margin of error for the confidence interval for gasoline mileage of make 2?

11. What was the lower 95% confidence limit for make 2 mileage?

12. What was the upper 95% confidence limit for make 2 mileage?

Conduct a test of the hypothesis that the mean mileage of makes 2 and 3 do not differ. Use the method for single means when σ is not known with the Error MS serving as the pooled variance.

Reminders: Test statistic t = difference of means / standard error of difference of means. The standard error of the difference equals square root of the sum of variances of the two means. The variance of each mean is estimated by the error mean square/number of observations in that mean.

13. What is the value of the t test statistic for testing the hypothesis that makes 2 and 3 do not differ in mileage?

A major flooding in a given year has a Poisson distribution with a mean occurrence of 2.5

d) How many months have to pass to be in the 80th percentile?

Thank you!!

If electricity power failures occur according to a Poisson distribution with an average of 3 failures every twenty weeks:

a) Calculate the probability that there will not be more than one failure during a particular week.

b) What is the distribution of the time between power failures?

c) What is the probability that the time between two power failures is between 15 and 30 weeks?

d) What is the probability that the time between two power failures is at least 40 weeks given that it has already been 20 weeks since the last failure?

4. An economist would recommend that the Bank of Canada change the interest rate for borrowed money if the average annual inflation rate is less than 2.15%. Based on a sample from the past 21 years, the average annual inflation rate was 1.87%, with a standard deviation of 0.67%. Assume the population is approximately normally distributed.

(a) [1 mark] Define the parameter you are testing.

(b) [1 mark] State the null hypothesis and alternative hypothesis you would use to test whether there was sufficient evidence that the average annual inflation rate was less than 2.15%.

(c) [1 mark] Assuming that H0 is true, what is the formula for the appropriate test statistic? How is it distributed? If it is t-distributed, be sure to indicate the number of degrees of freedom.

(d) [1 mark] Compute the observed value of the test statistic.

(e) [2 marks] Determine the p-value to within table accuracy. If your test statistic is zdistributed, this will be an exact value; if your test statistic is t-distributed, indicate the tightest possible bounds on the p-value.

(f) [1 mark] Report the strength of the evidence against H0 in favour of H1.

(g) [1 mark] Report the estimated value of the parameter and the estimated standard error.

(h) [2 marks] Would you reject your null hypothesis H0 when using a significance level of α = 0.01? Write a concluding sentence about the economist’s decision regarding the mean annual inflation rate.

My commute to university, follows a NORMAL distribution with a 35.5 minutes as mean and a standard deviation of 2.5 min. If my commute starts at 8:20 am and ideally I must be at university by 9am.

Define two random variables and formulate two questions, one involving binomial distribution and the other involving geometric distribution.

3. The following frequency table summarizes the distances in miles of 120 patients from a regional hospital. Distance Frequency 0-4 40 4-8 30 8-12 20 12-16 20 16-20 10 Calculate the sample variance and standard deviation for this data (since it is a case of grouped data- use group or class midpoints in the formula in place of X values, and first calculate the sample mean).

Describe an application of multivariate statistical analysis that is specific to your industry(Education or Scientific Research) or to your academic interests(data science). Explain why this technique is suitable in terms of measurement scale of variables and their roles.

1. Chapter 14: Exercise 4 on page 462

Groceries: A grocer store’s receipts show that Sunday customer purchases have a skewed distribution with a mean of $ standard deviation of $20

A) Explain why you cannot determine the probability that the next Sunday customer will spend at least $40.00.

B) Can you estimate the probability that the next 10 Sunday customers will spend an average of at least $40.00

C) Is it likely that the next 50 Sunday customers will spend an average of at least $40.00 Explain.

A simple random sample was taken of 44 water bottles from a bottling plant’s warehouse. The dissolved oxygen content (in mg/L) was measured for each bottle, with these results: 11.53, 8.35, 11.66, 11.54, 9.83, 5.92, 7.14, 8.41, 8.99, 13.81, 10.53, 7.4, 6.7, 8.42, 8.4, 8.18, 9.5, 7.22, 9.87, 6.52, 8.55, 9.75, 9.27, 10.61, 8.89, 10.01, 11.17, 7.62, 6.43, 9.09, 8.53, 7.91, 8.13, 7.7, 10.45, 11.3, 10.98, 8.14, 11.48, 8.44, 12.52, 10.12, 8.09, 7.34

Here the sample mean is 9.14 mg/L.

The population standard deviation of the dissolved oxygen content for the warehouse is known from long experience to be about σ = 2 mg/L.

Consider testing H0 : µ = 10 vs. HA : µ 6= 10, where µ is the unknown population mean dissolved oxygen content, at significance level α = .02 (not the usual .05).

(a) A Z test is appropriate here because we have a SRS with a large n. Find the value of the test statistic and the p-value

(b) What conclusion do you reach?

In a survey of 356 randomly selected gun owners, it was found that 82 of them said they owned a gun primarily for protection.

Find the margin of error and 95% confidence interval for the percentage of all gun owners who would say that they own a gun primarily for protection. Round all answers to 3 decimal places.

Margin of Error (as a percentage): %
Confidence Interval: % to %