Public safety officers are interested in how safe students feel when walking around campus late at night. They sample 20 students, asking them to rate their fear any number between 0 (no fear) and 10 (extreme fear). Below are their results:

1          0          2.5       5          3          7          4          5          6          5.5

6          2          1          0          3.5       5.5       5          3          4          3

A. What is the mean level of fear?

14. What is the standard deviation for their data? Show your calculations for full credit.

B. What is the median level of fear?

C. For participants with a score of 0, what is their z score? Show your calculations for full credit.

D. If the officers had a data point with a z score of 2.50, what would be the actual score? Show your calculations for full credit.

Please indicate which type of sampling design is most appropriate for each of the following studies. The choices are SRS, stratified random sampling, and matched pair design.

(1). A researcher wants to know the effect of climate change on the percent yield of the corn harvest. They collected the data for the same 50 plots in both 2016 and 2017 for their study.

(2).A developer in West Lafayette wants to know if students who are renting off-campus like their apartment complex. They chose 10 students who lived in 5 different complexes.

(3).A pharmaceutical company wants to determine if the size of a new pill is too large to take. They randomly select 200 people and asked if they could swallow the pill or not.

(4).A rice manufacturer chose 100 single servings to test to be sure that there is no more 10 ppb of arsenic in them to assure to their customers that the product is safe to eat.

A baby food company claims that on the average the product contains 6.0 grams of protein per bottle. A random sample of 14 bottles of the product was taken and the protein measurements are as follows. 5.1 4.9 6.0 6.4 5.7 4.8 6.2 6.0 5.9 5.6 5.5 5.8 5.3

(i) Find the sample mean x¯ and the sample standard deviation s.

(ii) Assume that the protein content per bottle obeys an N (µ, σ2) distribution with σ unknown. Give the study’s objective in terms of H0 and HA and then perform a test at the α = 0.05 level.

(iii) In the foregoing analysis (you just performed) you might reject H0 even when the mean protein content is exactly 6.0 gram per bottle as claimed. What is the name for this kind of mistake? What measure can be taken to control the probability of this kind of mistake?

17.35 Hand Size. A clever way to determine hand size in three dimensions is to measure the volume in ml of water displaced when the hand is dipped in a water container. A study used this method to gather hand volumes of 12 male college students. Here are the measurements:

400, 360, 420, 520, 460, 350, 500, 420, 450, 430, 395, 400

We consider this an SRS of all male college students. Obtain a 95% confidence interval for the mean hand size and interpret it in context.

Question 1:

Suppose you draw a sample of four skittles (with replacement) from a large jar containing 5,333 skittles. You record whether each of the four skittles is ORANGE or NOT ORANGE on each draw.  There are 955 orange skittles in the jar.

What is the probability of drawing an orange skittle from the jar? Round to two decimal places.

Question 2:

Suppose you draw a sample of four skittles (with replacement) from a large jar containing 5,333 skittles. You record whether each of the four skittles is ORANGE or NOT ORANGE on each draw.  There are 955 orange skittles in the jar.

Using your answer from Question #1, what is the probability of drawing no orange skittles in four draws? Round to two decimal places.

Question 3:

Suppose you draw a sample of four skittles (with replacement) from a large jar containing 5,333 skittles. You record whether each of the four skittles is ORANGE or NOT ORANGE on each draw.  There are 955 orange skittles in the jar.

Using your answer from Question #1 and #2, what is the probability of drawing no more than 1 orange skittle in four draws? Round to two decimal places.

Question 4:

Suppose you draw a sample of four skittles (with replacement) from a large jar containing 5,333 skittles. You record whether each of the four skittles is ORANGE or NOT ORANGE on each draw.  There are 955 orange skittles in the jar.

Use your answer from Question #1 to calculate the expected number of orange skittles in four draws. Round to two decimal places.

Question 5:

Suppose you draw a sample of four skittles (with replacement) from a large jar containing 5,333 skittles.  You record whether each of the four skittles is ORANGE or NOT ORANGE on each draw.  There are 955 orange skittles in the jar.  

Use your answer from Question #1 to calculate the standard deviation for the number of orange skittles in four draws. Round to two decimal places.

A researcher wants to test the efficacy of a drug called Ozempic for curbing hunger and thus promoting weight loss. The researcher believes that feelings of hunger will decrease after taking Ozempic. The researcher recruits 5 people to participate. They rate their hunger before taking a dose of Ozempic and then rate it again after taking Ozempic. The data are provided below. Test their hypothesis using the 5-step hypothesis testing procedure. Report your answers for each step by filling in the blanks below. Use a=0.05. Please post the answers to all 5 steps:

Step 1: The researcher's hypothesis is  (type your answer as: 1-tailed or 2-tailed):

Step 2: t obtained=  (type your answer with 2 decimal places)

Step 3: t critical=  (type your answer with 3 decimal places; report 2 critical values if necessary)

Step 4: Make your comparison. No need to write anything here.

Step 5: Type your final numerical answer in APA format:

and then type your conclusion:

a.Explain intuitively what does population mean and variance tells you about the distribution of a random variable?

b.Can you think of a reason why do we mostly only care about mean and variance a random variable since the distribution function could involve more than the two parameters?

c.Explain why we could use a sample data to draw conclusions about a population parameter?

d.Is p-value of a hypothesis test a random variable, why?

e.If you reject your null hypothesis, you have proved that the null hypothesis is wrong. Is this a correct statement, why?

A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 430 gram setting. It is believed that the machine is overfilling the bags. A 38 bag sample had a mean of 432 grams. Assume the population standard deviation is known to be 29. Is there sufficient evidence at the 0.02 level that the bags are overfilled?

Step 1 of 6:

State the null and alternative hypotheses.

Step 2 of 6:

Find the value of the test statistic. Round your answer to two decimal places.

Step 3 of 6:

Specify if the test is one-tailed or two-tailed.

Step 4 of 6:

Find the P-value of the test statistic. Round your answer to four decimal places.

Step 5 of 6:

Identify the level of significance for the hypothesis test.

Step 6 of 6:

Make the decision to reject or fail to reject the null hypothesis.

A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 401401 gram setting. It is believed that the machine is overfilling the bags. A 4242 bag sample had a mean of 408408 grams. Assume the population standard deviation is known to be 2121. Is there sufficient evidence at the 0.050.05 level that the bags are overfilled?

Step 1 of 6: State the null and alternative hypotheses.

Step 2 of 6: Find the value of the test statistic. Round your answer to two decimal places.

Step 3 of 6: Specify if the test is one-tailed or two-tailed.

Step 4 of 6: Find the P-value of the test statistic. Round your answer to four decimal places.

Step 5 of 6: Identify the level of significance for the hypothesis test.

Step 6 of 6: Make the decision to reject or fail to reject the null hypothesis.

What can you conclude from the null hypothesis test on the linear contrast between the IR group and the other two groups (DR1, DR2)?

Select ALL that APPLY and Explain

A- The linear contrast was statistically significant at the .10 level of significance.

B- There was no statistically significant difference, at the .05 alpha level, in the population between the IR group and the other two groups.

C-The linear contrast was statistically significant at the .05 alpha level of significance.

D- The difference in average ratings in the population, for the IR group was significantly different at the .05 alpha level, from the other two groups combined.

E- The difference in average ratings, in the population, for the IR group was significantly different, at the .05 alpha level, from either one of the other two groups.

The U.S. Department of Agriculture (USDA) uses sample surveys to produce important economic estimates. One pilot study estimated durum wheat prices in July and in January using independent samples of wheat producers in the two months.

The data is given below.

Although there is variation among prices within each month, the top four prices are all from July and the four lowest prices are from January. You will run a significance test to check that if the difference between months is just by chance. You’ll use α = 0.05 for significance test. Assume that the two Normal population distributions have the same standard deviation.

1. 1. Write out the null and alternative hypothesis associated with the research question. (2p)
2. 2. What type of statistical test will you use to answer the proposed research question? (Note: Is this a z-test or a t-test? (2p)
3. 3. What is the critical value at the 0.05 level of significance? Be sure and include whether this critical value is a z or t value and, if appropriate, include the degrees of freedom associated with this statistical test. (4p)
4. 4. What is the calculated value of the test statistic? (4p)
   5. What decision should be made about the null hypothesis? In other words, should you reject or retain the null hypothesis? (3p)
   6. Provide a brief conclusion regarding your findings. Use your powerpoint lecture slides for writing out the interpretation of your results. (5p)
   7. Show your Excel output (10p)

The director of research and development is testing a new medicine. She wants to know if there is evidence at the 0.01 level that the medicine relieves pain in less than 348 seconds. For a sample of 14 patients, the average time in which the medicine relieved pain was 343 seconds with a variance of 484. Assume the population distribution is approximately normal.

Step 1 of 5: State the null and alternative hypotheses

Step 2 of 5: Find the value of the test statistic. Round your answer to three decimal places.

Step 3 of 5: Specify if the test is one-tailed or two-tailed.

Step 4 of 5: Determine the decision rule for rejecting the null hypothesis. Round your answer to three decimal places.

Step 5 of 5: Make the decision to reject or fail to reject the null hypothesis.

A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 403 gram setting. It is believed that the machine is underfilling the bags. A 38 bag sample had a mean of 400 grams. Assume the population standard deviation is known to be 11. Is there sufficient evidence at the 0.01 level that the bags are underfilled?

Step 1 of 6: State the null and alternative hypotheses.

Step 2 of 6: Find the value of the test statistic. Round your answer to two decimal places.

Step 3 of 6: Specify if the test is one-tailed or two-tailed.

Step 4 of 6: Find the P-value of the test statistic. Round your answer to four decimal places.

Step 5 of 6: Identify the level of significance for the hypothesis test.

Step 6 of 6: Make the decision to reject or fail to reject the null hypothesis.

The owner of a departmental store would like to estimate monthly gross revenues as a function of advertising
expenditures. Historical data for randomly selected 8 months is given below (₹ in crores)
Monthly revenue Television Advertising Newspaper advertising

a. Derive a regression equation with amount of expenditure on television advertising as independent
variable.
b. Derive a regression equation with both expenditure on television advertising and newspaper advertising
as independent variables.
c. Estimate the monthly gross revenue for a month when 4 crores is spent on TV , and 1.5 crores is spent
on newspaper advertising.

In a study about undergraduate student credit card usage, it was reported that undergraduate students have a mean credit card balance of $3173 (Sallie Mae, April 2009). This figure was an all-time high and had increased 44% over the previous five years. Assume that a current study is being conducted to determine if it can be concluded that the mean credit card balance for undergraduate students has continued to increase compared to the April 2009 report. Based on previous studies, assume a population standard deviation of 1100.

Suppose you look at a random sample of 96 undergraduate students with a sample mean credit card balance of $3498.6.

You wish to test the claim that the mean credit card balance is higher than it was in 2009 at the α=α=0.005 level.

What is the t stat

what is the p value equal to.