PHA 6935 Applied Statistics. PHA 6935 Applied Statistics.

The distribution of grades for various classes taught by different professors is given in the following table. Test the null hypothesis that the grade distributions are homogenous for these three professors at a significance level of α = 0.05. (11 marks)

Professor

Grade

Einstein

Rutherford

Bohr

A

18

36

20

B

25

44

15

C

85

73

82

D

17

12

8

Define in your own words the following words: (4 marks)Sensitivity

Specificity

Accuracy

Test of homogeneity

Determine the sensitivity, specificity, and accuracy for the following analytical test data that detected the presence of morphine using the Marquis test. (5 marks)

Expected resultspositive conditionnegative conditionActual morphine presencepositive outcome152negative outcome423Would you conclude that the test is able to detect both true positive and true negative samples? Provide support for your answer.

The number of violent crimes reported to police on random selected days for 3 different cities is shown in the following table. Formulate the null and alternative hypothesis and calculate the F-test statistic. Use a significance level of α = 0.05 to reach a conclusion. [9 points]

CityNew AmsterdamOld BrusselsFuture Toronto5289412121103133979761413 The following ANOVA table is provided. [4 points]

Source of variationDegrees of freedomSum of squaresBetween4200Within453547 Calculate the following values assuming that all groups have the same sample size:

MSB and MSW

Number of groups and number of samples in each group

F-test statistic

Fcrit for α = 0.05. What is the conclusion?

Four catalysts that may affect the concentration of one component in a three-component liquid mixture are being investigated. The following concentrations are obtained. [12 points]

Catalyst123458.256.350.152.957.254.554.249.958.457.055.450.055.855.3 51.754.9 Determine if the 4 catalysts yield the same concentration of the component. If they do not, then use a post-hoc multiple comparison of your choice to determine which pairs of catalysts are different. Use a significance level of α = 0.05 for all your calculations.

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## stats question

Weight IAT Variables for Question 3

Quantitative Variable IAT-Weight-Score: Score on the Weight IAT

Categorical Variable (choose one) Birth-Gender: 1=Male; 2=Female OR Ethnicity: 1=Hispanic or Latinx; 2=Not Hispanic or Latinx (ignore 3=unknown)

Weight IAT variable descriptions (opens in a new tab).

Question 1

Which IAT data set are you working with?

Use StatCrunch and your unique IAT sample to estimate the mean age for the population of IAT participants at the 90% confidence level. Copy the contents of your StatCrunch output window and paste it into your response. (No need to type anything here – just copy and paste the contents of your StatCrunch output window.)

Are conditions met to estimate the mean age for the population of IAT participants? (Be sure to support your answer as demonstrated throughout Unit 8.)

State the confidence interval, and then interpret the confidence interval in context.

What is the margin of error (MOE)?

Which would be more accurate, the 90% confidence interval you found or an 85% confidence interval? Briefly explain. Which would be more precise? Briefly explain.

Question 2

At the end of 2020, the mean age of the U.S. population was estimated to be 38.5 years old. You are tasked with determining whether the mean age of the population of IAT participants (for your chosen IAT data set) differs from the mean age of the U.S. population.

Let be the mean age of the population of IAT participants for your chosen IAT data set. State the hypotheses (symbolically and in words). Include a clear description of the populations and the variable.

Use StatCrunch to create a histogram for the age distribution in your unique IAT sample. Download the StatCrunch output window and embed your histogram with your response. Can we safely use the t-test with your IAT sample? Explain.

Perform the t-test using StatCrunch. Copy the information from the StatCrunch output window and paste it into your response.

Based on the P-value, state your conclusions in context. Use a 5% level of significance. (NOTE: Since StatCrunch correctly calculates the P-value for either a one-tailed or a two-tailed test, you do not need to change the StatCrunch P-value.)

Using the context of this scenario, explain the meaning of each of following items from the StatCrunch output for the hypothesis test. Std. Err (standard error) T-stat (T-score) P-value

Question 3

Prepare to work through Question 3

See the Variables for Question 3 Only section above to learn which variables to use for your chosen IAT data set.

Choose only one of the categorical variables listed for your chosen IAT data set and note the two groups for your chosen categorical variable.

Here is the question to be investigated for the two groups in your chosen categorical variable. Do the population of IAT participants in one group score higher on the IAT test than the population of IAT participants in the other group?

To answer the question we are investigating, respond to each of the following

Use StatCrunch to determine the sample size and sample mean, , for the two groups in your chosen categorical variable (directions).Copy your StatCrunch output table and paste into your response. Then relabel the categorical variable groups with the appropriate word(s), i.e. replace the group numbers with the appropriate word(s) to describe the group (see the Categorical Variable section above for your data set).

Which of the two groups has the smallest sample mean? Which has the largest sample mean?

Let ?1?1 be the population mean for the group with the largest sample mean. Let ?2?2 be the population mean for the group with the smallest sample mean. State the null and alternative hypotheses (symbolically and in words). Include a clear description of the populations and the variable.

To test your hypotheses, is it appropriate to use the two-sample T-test? If so, explain why and provide any supporting evidence. If not, start over and choose the other categorical variable listed with your chosen IAT data set.WARNING: If it is not appropriate to use the two-sample T-test for either of the categorical variables listed with your IAT data set, something may be wrong. Stop and contact me as soon as possible.

Proceed only if it is appropriate to use the two-sample T-test.

Use StatCrunch to carry out the test. (directions) Copy the content in the StatCrunch output window (text and the table) and paste it into the textbox as your response to this item.

Use a 5% significance level to state a conclusion. Be sure to state your conclusion in context and in terms of what a “more positive score” on the IAT means for your data set. (Hint: in the variables section above, click on the variable descriptions link for your data set. The variable descriptions page opens in a new window. Review the Interpreting the IAT section at the top of that page.)

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