You took independent random samples of 20 students at City College and 25 students at SF State. You asked each student how many sodas they drank over the course of a year. The sample mean at City College was 80 and the sample standard deviation was 10. At State the sample mean was 90 and the sample standard deviation was 15. Use a subscript of c for City College and a subscript of s for State.

1. Calculate a point estimate of the difference between the two population means.

2. Calculate the appropriate number of degrees of freedom to use for your analysis. Hint: Remember that you always round down for degrees of freedom if you get a decimal answer. Note: To calculate this answer you must use the formula which assumes unequal variances.

3. Determine a 95% confidence interval for the difference between the two population means.

4. Give the null and alternative hypotheses for a hypothesis test to test to see if there is a statistically significant difference in the population means between students at the two schools.

5. State α using the confidence level in question 3.

6. Calculate the value of the test statistic.

7. Find a range for the p-value.

8. What is your conclusion in statistical terms?

9. Explain the meaning of this conclusion in business terms.

10. What statistical conclusion would you reach using the confidence interval approach? Explain how you reach this conclusion. Is it the same conclusion you reached using the p-value approach?

Chi-Square Analysis Worksheet MTH 160: Statistics

Suppose the local state university wants to determine whether there is a relationship between a student’s gender and a student’s major in college. The registrar was asked to randomly select 55 students and record their gender and major. The majors were grouped into categories of Natural Science (NS), Social Sciences (SS), and Humanities (H). Answer the following questions based on the results in the table below.

NS SS H Total

Men 11 9 3 23

Wom 9 13 10 32

Total 20 22 13 55

Part I: 1. Determine the expected frequency for each of the cells within the table.

2. Compute the sample chi-square statistic from the contingency table. 3. Conduct a chi-square test of independence to determine whether there is a relationship between gender and college majors. Show all of your work to support your chi-square test. 4. What conclusion can be determined from the results of the chi-square test? Part II:

Suppose we are only interested in the college majors of the women in our study. We would like to compare our sample to the national percentage of women majoring in each of the categories (NS, SS, and H) and determine whether the sample distribution fits the national distribution. Suppose the national percentage of women majoring in Natural Sciences is 22%, majoring in Social Sciences is 28%, and majoring in the Humanities is 30%.

NS SS H Total

Women 9 13 10 32

1.Conduct a chi-square goodness-of-fit test to determine whether our sample data fits the national distribution. Show all of your work to support your chi-square test.

2. What conclusion can be determined from the results of the chi-square test?

Data

Phase 1 report must include the preliminary findings:

1. What are the means, medians, modes, range and standard deviation for each of the six car models? Draw box plots.
2. What are the means, medians, modes, range and standard deviations for each of the six months (May – October)? Draw box plots.

Explain the contribution of the Milan Group to family therapy theory.

A transect is an archaeological study area that is 1/5 mile wide and 1 mile long. A site in a transect is the location of a significant archaeological find. Let x represent the number of sites per transect. In a section of Chaco Canyon, a large number of transects showed that x has a population variance σ² = 42.3. In a different section of Chaco Canyon, a random sample of 20 transects gave a sample variance s² = 46.5 for the number of sites per transect. Use a 5% level of significance to test the claim that the variance in the new section is greater than 42.3. Find a 95% confidence interval for the population variance.

(a) What is the level of significance?


State the null and alternate hypotheses.

H_o: σ² = 42.3; H₁: σ² ≠ 42.3 H_o: σ² = 42.3; H₁: σ² > 42.3     H_o: σ² = 42.3; H₁: σ² < 42.3 H_o: σ² > 42.3; H₁: σ² = 42.3

(b) Find the value of the chi-square statistic for the sample. (Round your answer to two decimal places.)


What are the degrees of freedom?


What assumptions are you making about the original distribution?

We assume a exponential population distribution. We assume a normal population distribution.     We assume a binomial population distribution. We assume a uniform population distribution.

(c) Find or estimate the P-value of the sample test statistic.

P-value > 0.100 0.050 < P-value < 0.100     0.025 < P-value < 0.050 0.010 < P-value < 0.025 0.005 < P-value < 0.010 P-value < 0.005

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis?

Since the P-value > α, we fail to reject the null hypothesis. Since the P-value > α, we reject the null hypothesis.     Since the P-value ≤ α, we reject the null hypothesis. Since the P-value ≤ α, we fail to reject the null hypothesis.

(e) Interpret your conclusion in the context of the application.

At the 5% level of significance, there is insufficient evidence to conclude conclude that the variance is greater in the new section. At the 5% level of significance, there is sufficient evidence to conclude conclude that the variance is greater in the new section.    

(f) Find the requested confidence interval for the population variance. (Round your answers to two decimal places.)

Interpret the results in the context of the application.

We are 95% confident that σ² lies outside this interval. We are 95% confident that σ² lies above this interval.     We are 95% confident that σ² lies below this interval. We are 95% confident that σ² lies within this interval.

Discuss validity and reliability as "confounding variables" and how can they negatively impact the results of a study? What are confounding variables? Try to provide an example to illustrate your point.

A poll surveyed people in six countries to assess attitudes toward a variety of alternate forms of energy. Suppose the data in the following table are a portion of the poll's findings concerning whether people favor or oppose the building of new nuclear power plants.

(a)

How large was the sample in this poll?

(b)

Conduct a hypothesis test to determine whether people's attitude toward building new nuclear power plants is independent of country.

State the null and alternative hypotheses.

H₀: The attitude toward building new nuclear power plants is not mutually exclusive of the country.
H_a: The attitude toward building new nuclear power plants is mutually exclusive of the country.H₀: The attitude toward building new nuclear power plants is not independent of the country.
H_a: The attitude toward building new nuclear power plants is independent of the country.    H₀: The attitude toward building new nuclear power plants is mutually exclusive of the country.
H_a: The attitude toward building new nuclear power plants is not mutually exclusive of the country.H₀: The attitude toward building new nuclear power plants is independent of the country.
H_a: The attitude toward building new nuclear power plants is not independent of the country.

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

Find the p-value. (Round your answer to four decimal places.)

p-value =

State your conclusion.

Do not reject H₀. We cannot conclude that the attitude toward building new nuclear power plants is independent of the country.Reject H₀. We conclude that the attitude toward building new nuclear power plants is not independent of the country.    Reject H₀. We cannot conclude that the attitude toward building new nuclear power plants is independent of the country.Do not reject H₀. We conclude that the attitude toward building new nuclear power plants is not independent of the country.

(c)

Using the percentage of respondents who "strongly favor" and "favor more than oppose," which country has the most favorable attitude toward building new nuclear power plants?

Great BritainFrance    ItalySpainGermanyUnited States

Which country has the least favorable attitude?

Great BritainFrance    ItalySpainGermanyUnited States

Use Excel to test. For each paired difference, compute After – Before. In Data Analysis, t-Test: Paired Two Sample for means, select the After data for Variable 1 Range. Note that the critical value output by Data Analysis for this test is always positive. In this problem, the sign of the critical value is negative corresponding to 1-tailed test with lower reject region and negative lower critical value.

           
   Person   Before   After
   1   176   164
   2   192   191
   3   185   176
   4   177   176
   5   196   185
   6   178   169
   7   196   196
   8   181   172
   9   158   158
   10   201   193
   11   191   185
   12   193   189
   13   176   175
   14   212   210
   15   177   173
   16   183   180
   17   210   204
   18   198   192
   19   157   152
   20   213   200
   21   161   161
   22   177   166
   23   210   203
   24   192   186
   25   178   170

What is your conclusion?

A. Do not reject the NULL Hypothesis because the actual value is greater than critical value

B. Reject the NULL Hypothesis because the actual value is less than the critical value

C. Reject the NULL Hypothesis because the actual value is greater than critical value

D. Do not reject the NULL Hypothesis because the actual value is less than the critical value

11. Assume that when adults with smartphones are randomly​ selected, 57​% use them in meetings or classes. If 20 adult smartphone users are randomly​ selected, find the probability that exactly 15 of them use their smartphones in meetings or classes.

The probability is _____

​(Round to four decimal places as​ needed.)

12. Assume that when adults with smartphones are randomly​ selected, 58​% use them in meetings or classes. If 10 adult smartphone users are randomly​ selected, find the probability that at least 7 of them use their smartphones in meetings or classes.

The probability is_____

​(Round to four decimal places as​ needed.)

13. A survey showed that 76​% of adults need correction​ (eyeglasses, contacts,​ surgery, etc.) for their eyesight. If 8 adults are randomly​ selected, find the probability that no more than 1 of them need correction for their eyesight. Is 1 a significantly low number of adults requiring eyesight​ correction?

The probability that no more than 1 of the 8 adults require eyesight correction is _____.

​(Round to three decimal places as​ needed.)

Perform t-test on eRPM for Strategy A and B. H0: A = B vs. H1: A != B (Two-sided t-test) What is the p-value?

Choose an organization (Amazon, Sony, etc.) and discuss how they manage large data sets including protocol for transferring data. Select one public data set and examine the technical format and how the data is manipulated globally.

You have 100 coins, and 99 of them are fair (equal probability of heads or tails). One of them is weighted and has a 90% probability of landing on heads. You randomly choose one of the 100 coins. Find the probability that it is a weighted coin, under the following scenarios: (Hint: if your calculator can’t compute 100!, R can, just type factorial(100))

(a) You flip it 10 times and lands on heads 10 times (b) You flip it 10 times and it lands on heads 9 times

(c) You flip it 20 times and it lands on heads 18 times (d) You flip it 100 times and it lands on heads 77 times

Consider the following data set.

a) plot the data (y versus x). Are there any points that appear to be outliers? If there are, circle them and label as such.

b) produce a regression of y against x. Add the regression line to the plot in a). Do you think that the regression line captures the most important features of the data set reasonably well?

c) using calculations at a 5% significance level, can you say that there is a significant linear relationship between the x and y? That is, can you say with 95% confidence that y linearly depends on x? Does this result agree with the conclusion you made in b)?

d) testing at a 5% significance level, can you say that the intercept (β0) is not zero? How does this conclusion agree with the plot in b)?

e) Assume that the first data point is an outlier (e.g. the value was misrecorded). Remove the outlier, and redo the parts b)-d). Plot the data set and both regression lines (before and after the outlier was removed). Comment on the difference. Also comment on the difference between the results of the tests in c) and d), if any.

Perform t-test on eRPM for strategy A and B. H0: A = B vs. H1: A != B (Two-sided t-test) What is the p-value?

#2. The operations manager of a musical instrument distributor feels that demand for a particular type of guitar may be related to the number of YouTube views for a popular music video by the popular rock group Marble Pumpkins during the preceding month. The manager has collected the data shown in the following table: YouTube Views (1000s) Guitar Sales 30 8 40 11 70 12 60 10 80 15 50 13

a. Graph the data to see whether a linear equation might describe the relationship between the views on YouTube and guitar sales.

b. Using the equations presented in this chapter, compute the SST, SSE, and SSR. Find the least squares regression line for the data.

c. Using the regression equation, predict guitar sales if there were 40,000 views last month.