What is a Hypothesis statement? And what is the Hypothesis Testing Process?​

1. A convenience store manager notices that sales of soft drinks are higher on hotter days, so he assembles the data in the table.

(a) Make a scatter plot of the data below.

(b) Sketch the best fit line and write the equation for that line.

Equation:______________________________________

(c) Use the model to predict soft-drink sales if the temperature is 95°F.

(d) Using the scatterplot, describe the association you see between the two variables. Guess your r, (Remember r is not the same as slope!) Make sure to mention direction and strength.

graph

College Graduation Rates. Data from the College Results Online website compared the 2011 graduation rate and median SAT score for 92 similar-sized public universities and colleges in the United States. The scatterplot below shows the relationship between these two variables along with the least squares fit. Round all calculated results to 4 decimal places.

1. The relationship between median SAT score and graduation rate is  ? positive negative ,  ? weak strong , and  ? linear non-linear .

2. The explanatory variable is  ? graduation rate median SAT college year  and the response variable is  ? graduation rate median SAT college year .

The summary statistics for graduation rate and median SAT score are listed below. The correlation between graduation rate and median SAT score is 0.663.

Median SAT score: mean = 1030.3, standard deviation = 80.7
Graduation rate: mean = 49.6, standard deviation = 14.3

3. The equation of the regression line is y =  +  x

4. Complete the following sentence to interpret the slope of the regression line:

An increase of  in Median SAT score corresponds to a/an  ? decrease increase  of  in Graduation Rate.

5. The recorded median SAT score for Northern Michigan University is 1026. Use the regression equation to estimate the graduation rate for Northern Michigan University.

6. The recorded graduation rate for Northern Michigan University is 46.3. Complete the following sentence.

The residual for Northern Michigan University is  . This means the graduation rate at Northern Michigan University is
A. lower than
B. higher than
C. the same as
the rate predicted by the regression model.

7. Stanford University (an elite private university in California not included in this data set) has a median SAT score of 1455. Would it be appropriate to use this linear model to predict the graduation rate for Stanford?

A. Yes, because 1455 is a reasonable median SAT score for an elite university.
B. No, because 1455 is beyond the range of the data used to build the regression model.
C. No, because 99.495% is too large to be a reasonable graduation rate, even for an elite university.

Vertical banded gastroplasty is a surgical procedure that reduces the volume of the stomach in order to produce weight loss. In a recent study, 82 patients with Type 2 diabetes underwent this procedure, and 59 of them experienced a recovery from diabetes. Does this study provide convincing evidence that more than 60% of those with diabetes who undergo this surgery will recover from diabetes? Use the α = 0.05 level of significance.

(SHOW WORK PLEASE FOR ME TO UNDERSTAND THE STEPS)

1. Compute the following

p-hat, Standard error, Critical Z, and Test Z.

2. Do you reject or fail to reject the null hypothesis. Explain why. Use the α = 0.05 level of significance.

3. State the null and alternative hypotheses and what type of TEST?

4. Compute the P-value?

A new industrial oven has just been installed at Piatt Bakery. To develop experience regarding the oven temperature, an inspector reads the temperature at four different places inside the oven each half hour starting at 8:00 a.m. The last reading was at 10:30 a.m., for a total of six samples. The first reading, taken at 8:00 a.m., was 337 degrees Fahrenheit. (Only the last two digits are given in the following table to make the computations easier.)

1. On the basis of this initial experience, determine the control limits for the range. (Round your intermediate calculations and final answers to 2 decimal places.)

2. For each time period, is the temperature out of control?

Thank you!!

The president of a University wishes to find the average age of students presently enrolled. From past studies, the standard deviation is known to be 2 years. A random sample of 50 students is selected and the mean is found to be 23.2 years.

A. Find the 95% confidence interval for the population mean.

B. Find the 99% confidence interval for the population mean?

1. Create a histogram using Excel’s Data Analysis toolpack for Friends. Use the Sturges’ rule to find how many bins you should include. In your Word file, make sure to in- clude both a frequency table for the histogram with bin limits, frequencies and relative frequencies, and your histogram chart. What can you say about the distribution of Friends? All calculations should be shown in excel. (Along with the answer, can anyone give me the instruction on how to do the histogram and solve the questions using excel?).

Test the claim about the population mean μ at the level of significance α. Assume the population is normally distributed.

Claim: μ ≠ 95; α = 0.05; s = 1.53
Sample statistics: x = 94.1, n = 12

The following table was presented in an article summarizing a study to compare a new drug to a standard drug and to a placebo.

*Table entries and Mean (SD) or % Are there any statistically significant differences in the characteristics shown among the treatments? Justify your answer. Consider the test for differences in age among treatments. Write the hypotheses and the formula of the test statistic used (No computations required – formula only). Consider the test for differences in insurance coverage among treatments. Write the hypotheses and the formula of the test statistic used (No computations required – formula only). Consider the test for differences in disease stage among treatments. Write the hypotheses and the formula of the test statistic used (No computations required – formula only).

Consider the following ANOVA experiment:

H₀: μ₁ = μ₂ = μ₃ = μ₄

with

n = 21,

a sample F statistic = 4.76, and

α = 0.025.

the data for the perceived level of stress of 30 employees and each employee’s number of absences in a 120-day period are shown.

a) Write the null and alternate hypotheses for the test you suggest conducting to test for significance of difference between the three levels of stress.

b) Conduct the appropriate statistical test on the data in the file. Interpret your findings.

c) Discuss the two kinds of variance here, and indicate how they are compared to conclude a significant difference.

1. In the 2008 General Social Survey, incomes of married respondents were classified as above average, average, and below average. Respondents also answered a question about marital happiness as not happy, pretty happy, or very happy. The results are below:

Conduct an appropriate test to determine whether or not there is a statistically significant association between marital happiness and income at the 5% significance level.

1. Which is the independent variable and which is the dependent variable?
2. For individuals with average income, what percentage of individuals report their marital happiness as “pretty happy?”
3. Are the basic assumptions of the hypothesis test satisfied?
4. What are the null and alternative hypotheses?
5. Based on the significance level at which you are testing, what is (are) the critical value(s) for the test?
6. Calculate the appropriate test statistic, showing all your work. You should explicitly display (1) expected values for each cell and (2) the test statistic contribution of each cell in addition to calculating the overall test statistic.
7. Calculate the corresponding p-value from the appropriate table or online calculator.
8. What conclusions can you draw from the hypothesis test? Be sure to comment on evidence from both the test statistic and p-value.

Suppose that during an unexpected snowstorm, Mr. Wong decided to take a random sample of students in his AP Statistics class to examine their arrival times, in minutes. He compared the difference between the students' arrival time with the time the class was supposed to begin.

Mr. Wong asks you, his assistant, to use the information below to answer the following questions (negative value means that the student arrived BEFORE class began).

* Please do not copy other experts' solutions, thank you!

Question A: Mr. Wong would like to determine if his students arrive to class late on average. He asks you to perform a hypothesis test @ 10% significance level. Clearly state the conclusion you would tell Mr. Wong using a critical value.

Question B:

i) Mr. Wong asks you to calculate a 90% confidence interval for the average difference in time.

ii) Interpret the interval you calculated.

iii) Based on the interval, what can you say about Mr. Wong's AP Statistics class's arrival time?

Question C: Did you expect the conclusion in Question B to be the same as the conclusion in Question A? Explain why or why not.

Suppose X has probability distribution

x: 0 1 2 3 4

P(X = x) 0.2 0.1 0.2 0.2 0.3

Find the following probabilities:

a. P(X < 2)

b. P(X ≤ 2 and X < 4)

c. P(X ≤ 2 and X ≥ 1)

d. P(X = 1 or X ≤ 3)

e. P(X = 2 given X ≤ 2)

The following data is representative of that reported in an article with x = burner-area liberation rate (MBtu/hr-ft²) and y = NO_x emission rate (ppm):

a. State the appropriate null and alternative hypotheses.

b. Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to three decimal places.)

c. Compute a 95% CI for the expected change in emission rate associated with a 10 MBtu/hr-ft² increase in liberation rate. (Round your answers to two decimal places.)