STA320: Introduction to Statistical Theory - Statistics Assignment Help

Assignment Task:

Q#1:

a) State the null and alternative hypothesis for a test to determine the validity of the claim 

b) Identify left, right, or two-tailed test type 

1. Speedy Solutions is a delivery company that claims all deliveries average less than 72 hours.

2. The average miniature horse is less than 34 inches at the shoulder. Tiny Equines claims that their miniature horses are an average of 3 inches fewer than the breed average.

3. The 2011 average service time for Fast Fatz Burgers was 56 seconds. The store manager claims that the 2012 average is more than 5 seconds faster.

4. About half of Chinese prefer to eat healthy food.

Q#2:

Blood glucose levels for obese patients have a mean of 100 with a standard deviation of 17. A researcher thinks that a diet high in raw cornstarch will have a positive or negative effect on blood glucose levels. A sample of 30 patients who have tried the raw cornstarch diet have a mean glucose level of 145.

1. What would the null and alternative hypotheses be for this scenario? 

2. What would the standard error be for this particular scenario? 

3. Describe in your own words how you would set the critical regions and what they would be at an alpha level of .05. 

4. Test the null hypothesis and explain your decision

Q#3:

You have just taken ownership of a pizza shop. The previous owner told you that you would save money if you bought the mozzarella cheese in a 4.5 pound slab on the average. Each time you purchase a slab of cheese, you weigh it to ensure that you are receiving a standard deviation of 72 ounces of cheese. The results of 7 random measurements are 70, 69, 73, 68, 71, 69 and 71 ounces. Are these differences due to chance or is the distributor giving you less cheese than you deserve? 

1. State the hypotheses. 

2. Calculate the test statistic. 

3. Would the null hypothesis be rejected at the 10% level? The 5% level? The 1% level?

Q#4:

A rowing team consists of four rowers who weigh 18, 24, and 36 pounds. Find all possible random samples with replacement of size three and compute the sample mean for each one. Use them to find the sampling distribution of the sample mean. Also verify the results.

Q#5:

Given the six-element population 8, 12, 15, 18, 21, 27, 32 and 36. How many samples of size 2 can be drawn, without replacement from this population? Compute the sampling distribution of the mean for samples of size 2. Compute the mean and standard deviation of this distribution. Also verify the results.

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