Hi I had question about finding the critical values of an independent, ,random, two sample test( assuming equality of variances)

The question:

Philosophical and health issues are prompting an increasing number of Taiwanese to switch to a vegetarian lifestyle. A study published in the Journal of Nutrition compared the daily intake of nutrients by vegetarians and omnivores living in Taiwan.Amongthe nutrients consideredwasprotein.Too little protein stunts growth and interferes with all bodily functions; too much protein puts a strain on the kidneys, can cause diarrhea and dehydration, and can leach calcium from bones and teeth. Independent random samples of 51 females vegetarians and 53 female omnivores yielded the following summary statistics, in grams, on daily protein intake. Vegetarians Omnivores ?? ̅̅̅̅ = ??. ?? ?? ̅̅̅̅ = ??. ?? s1 = 18.82 s2 = 18.97 n1 = 51 n2 = 53 Do the data provide sufficient evidence to conclude that the mean daily protein intakes of female vegetarians and female omnivores differ? Perform the required hypothesis test at the 1% significance level. Assume equality of variances.

An engineer designed a valve that will regulate water pressure on an automobile engine. The engineer designed the valve such that it would produce a mean pressure of 5.95.9 pounds/square inch. It is believed that the valve performs above the specifications. The valve was tested on 110110 engines and the mean pressure was 6.06.0 pounds/square inch. Assume the variance is known to be 0.360.36. A level of significance of 0.10.1 will be used. Determine the decision rule.

Enter the decision rule.

Evaluate the data provided in the table below.

a) Test the hypothesis that the population mean is equal to 55, compared to the mean is not equal to 55 if alpha is 0.10.

b) Find the p-value.

c) Compute the power of the test if the true mean is 50.

A coin is flipped 34 times and heads is observed 22 times. Assuming this proportion is normal for this particular​ coin, if the coin is flipped 50​ times, what is the probability that heads is observed at least 25​ times?

The probability is:

(Round to 4 decimal places)

The mean height of women in a country​ (ages

20minus−​29)

is

64.3

inches. A random sample of

65

women in this age group is selected. What is the probability that the mean height for the sample is greater than

65

​inches? Assume

sigmaσequals=2.69

The probability that the mean height for the sample is greater than

65

inches is

A data set is given

a)

(a) Draw a scatter diagram. Comment on the type of relation that appears to exist between x and y.

​(b) Given that

x overbarxequals=3.83333.8333​,

s Subscript xsxequals=2.40142.4014​,

y overbaryequals=3.98333.9833​,

s Subscript ysyequals=1.74521.7452​,

and

requals=negative 0.9457−0.9457​,

determine the​ least-squares regression line.

​(c) Graph the​ least-squares regression line on the scatter diagram drawn in part​ (a).

A particular fruit's weights are normally distributed, with a mean of 520 grams and a standard deviation of 40 grams.

If you pick 27 fruits at random, then 11% of the time, their mean weight will be greater than how many grams?

1) Imagine you are explaining to your friend how Type I and Type II errors work. You friend then asks you, “Why don’t researchers just set the alpha error rate really low (like .01%) every time so the odds they make a Type I error are very small?” Explain to your friend why scientists don’t set the alpha error rate to a very small value every time they do research. Can you think of a reason why a scientist would consider setting the alpha error rate to a smaller value than the traditional .05? Provide an example that illustrates your reasoning. Your example can be a hypothetical or real situation. NOTE: Do NOT reuse any examples I provided in the Chapter 9 video lectures.

Use duality to answer the following application.

Oz makes lion food out of giraffe and gazelle meat. Giraffe meat has 18 grams of protein and 36 grams of fat per pound, while gazelle meat has 36 grams of protein and 18 grams of fat per pound. A batch of lion food must contain at least 28,800 grams of protein and 43,200 grams of fat. Giraffe meat costs $1 per pound and gazelle meat costs $2 per pound. How many pounds of each should go into each batch of lion food in order to minimize costs? HINT [See Example 2.]

(giraffe meat, gazelle meat) =

What are the shadow costs of protein and fat? lb

protein$  per g

fat$  per g

Audrey and Diana go fishing at the Lyndon Fishing Pond. Upon arrival the owner informs them that the pond is stocked with an infinite number of independent fish, and that a typical fisher catches fish at a Poisson rate of 2 fish per hour. There are 8 other people fishing there that day. Diana has the same skill level as a typical fisher but Audrey catches on average twice as many fish as a typical fisher.

For the rest of the question, assume that 100 fish were caught that day.

Use those rounded probabilities in parts b), c) and d):
i. The probability a fish was caught by Audrey is 0.182
ii. The probability a fish was caught by Diana is 0.091
iii. The probability a fish was caught by someone else is 0.727

(c) (2) Find the probability that Audrey catches 15 fish and Diana catches 15 fish

(d) (2) Find the probability that Audrey and Diana catch 30 fish together

(e) (2) Given that Audrey catches 15 fish, find the probability that Diana catches 15 fish

(f) (2) Explain logically the difference between the probabilities in (c), (d), and (e)

The incubation time for a breed of chicks is normally distributed with a mean of 24 days and standard deviation of approximately 3 days. Look at the figure below and answer the following questions. If 1000 eggs are being incubated, how many chicks do we expect will hatch in the following time periods? (Note: In this problem, let us agree to think of a single day or a succession of days as a continuous interval of time. Assume all eggs eventually hatch.) (a) in 18 to 30 days 950 chicks (b) in 21 to 27 days chicks (c) in 24 days or fewer chicks (d) in 15 to 33 days

1. An online retailer ships products from overseas with an advertised delivery date within 10 days. To test whether or not deliveries are made within the advertised time, a random sample of 36 orders is selected from a normal population. The sample mean delivery time is 12 days, and the known population standard deviation is 3 days. Conduct the following test of hypothesis using the 0.01 significance level:                                                                                 [4 Marks]

H₀: µ ≤ 10

H₁: µ > 10

1. An online retailer ships products from overseas with an advertised delivery date within 10 days. To test whether or not deliveries are made within the advertised time, a random sample of 36 orders is selected from a normal population. The sample mean delivery time is 12 days, and the known population standard deviation is 3 days. Conduct the following test of hypothesis using the 0.01 significance level:                                                                                 

H₀: µ ≤ 10

H₁: µ > 10

A study of the effect of television commercials on 12-year-old children measured their attention span, in seconds. The commercials were for clothes, food, and toys.

1. Complete the ANOVA table. Use 0.05 significance level. (Round the SS and MS values to 1 decimal place and F value to 2 decimal places.)

2. Find the values of mean and standard deviation. (Round the mean and standard deviation values to 3 decimal places.)

3. Is there a difference in the mean attention span of the children for the various commercials?

4. Are there significant differences between pairs of means?

Wildlife biologists inspect 150 deer taken by hunters and find 26 of them carrying ticks that test positive for Lyme disease.

a.) Create a​ 90% confidence interval for the percentage of deer that may carry such ticks.( __%,__%)

b.) If the scientists want to cut the margin of error in​ half, how many deer must they​ inspect?

c.)  What concerns do you have about this​ sample?

The owner of Showtime Movie Theaters, Inc., would like to predict weekly gross revenue as a function of advertising expenditures. Historical data for a sample of eight weeks follow.

(a)

Develop an estimated regression equation with the amount of television advertising as the independent variable. (Round your numerical values to two decimal places. Let x₁ represent the amount of television advertising in $1,000s and y represent the weekly gross revenue in $1,000s.)

ŷ =

(b)

Develop an estimated regression equation with both television advertising and newspaper advertising as the independent variables. (Round your numerical values to two decimal places. Let x₁ represent the amount of television advertising in $1,000s, x₂ represent the amount of newspaper advertising in $1,000s, and y represent the weekly gross revenue in $1,000s.)

ŷ =