Statistics

EXERCISE 2. Anna Sheehan is the manager of the Spendwise supermarket chain. She would like to be able to predict paperback book sales (books per week) based on the amount of shelf display space (in feet) provided. Anna gathers data for a sample of 11 weeks.

a) Plot a scatter diagram b) What kind of relationship exists between these two variables? c) Compute the correlation coefficient. d) Determine the sample regression equation e) Estimate paperback book sales for a week in which 4 feet of shelf space are provided. Answer. b) positive c) 0,95 d) Y = 36,4053X + 32,4576 e) 178,0779.

EXERCISE 3. A random sample of 5 families shows the following information concerning annual family income and annual expenditure on durable goods (refrigerators, washing machines, stereos and so on):

a) Determine the estimated regression equation Y = aX + b; b) Estimate the annual expenditure on durable goods of a family earning 12000 euros per year. Answer. a) Y = 0,31X – 0,79; b) 293 euros.

Please show your workings, I have provided you with the possible answers but they might be wrong as well due our book. Thank you in advance!

Is there a relationship between confidence intervals and two-tailed hypothesis tests? Let c be the level of confidence used to construct a confidence interval from sample data. Let α be the level of significance for a two-tailed hypothesis test. The following statement applies to hypothesis tests of the mean.

For a two-tailed hypothesis test with level of significance α and null hypothesis H₀: μ = k, we reject H₀ whenever k falls outside the c = 1 – α confidence interval for μ based on the sample data. When k falls within the c = 1 – α confidence interval, we do not reject H₀.

(A corresponding relationship between confidence intervals and two-tailed hypothesis tests also is valid for other parameters, such as p, μ₁ − μ₂, or p₁ − p₂, which we will study in later sections.) Whenever the value of k given in the null hypothesis falls outside the c = 1 – α confidence interval for the parameter, we reject H₀. For example, consider a two-tailed hypothesis test with α = 0.01 and

H₀: μ = 21
H₁: μ ≠ 21

A random sample of size 22 has a sample mean x = 19 from a population with standard deviation σ = 6.

(a) What is the value of c = 1 − α?


Using the methods of Chapter 7, construct a 1 − α confidence interval for μ from the sample data. (Round your answers to two decimal places.)

What is the value of μ given in the null hypothesis (i.e., what is k)?
k =

Is this value in the confidence interval?

Yes No    

Do we reject or fail to reject H₀ based on this information?

Fail to reject, since μ = 21 is not contained in this interval.

Fail to reject, since μ = 21 is contained in this interval.    

Reject, since μ = 21 is not contained in this interval.

Reject, since μ = 21 is contained in this interval.

(b) Using methods of Chapter 8, find the P-value for the hypothesis test. (Round your answer to four decimal places.)


Do we reject or fail to reject H₀?

Reject the null hypothesis, there is sufficient evidence that μ differs from 21. Fail to reject the null hypothesis, there is insufficient evidence that μ differs from 21.     Fail to reject the null hypothesis, there is sufficient evidence that μ differs from 21. Reject the null hypothesis, there is insufficient evidence that μ differs from 21.

Compare your result to that of part (a).

We rejected the null hypothesis in part (a) but failed to reject the null hypothesis in part (b). These results are the same.     We rejected the null hypothesis in part (b) but failed to reject the null hypothesis in part (a).

The Graded Naming Test (GNT) asks respondents to name objects in a set of 30 black and white drawings in order to detect brain damage. The GNT population norm for adults in England is 20.4. Researchers wondered whether a sample for Canadian adults had different scores from adults in England (Roberts, 2003). If the scores were different, the English norms would not be valid for use in Canada. The mean for 30 Canadian adults was 17.5. Assume that the standard deviation of the adults in England is 3.2. How can we calculate a 95% Confidence Interval (CI) for these data?

1. Calculate a 95% CI and a 90% CI for this data.
2. Are the English norms valid for use in Canadian use? Explain how you know your answer to be true.
3. How do the two CI’s (95% and 90%) compare to one another?
4. What is the effect size for these data?
5. What does this effect size indicate about the meaningfulness of this test for Canadians?
What would you recommend doing to increase the power of this experiment?

Statistics

EXERCISE 8. A fair pair of dies is to be cast once. What is the probability of getting a) 7, b) 11, c) 7 or 11, d) a sum divisible by 3? Answer. a) 1/6. b) 1/18. c) 2/9. d) 1/3. EXERCISE 9.One card is selected from an ordinary deck of playing cards. What is the probability of getting a) a queen, b= a jack, c= either a queen or a jack, d) a queen or a red card, e) a face card? Answer. a) 4/52. b) 4/52. c) 8/52. d) 28/52. e) 12/52.

EXERCISE 10. In a certain community, the probability that a family has a television set is 80%; a washing machine 50%; both a television set and a washing machine 45%. What is the probability that a family has either a television set or a washing machine or both? Answer. 85%.

EXERCISE 11. In a state lottery, a three-digit number is randomly selected between 000 and 999 inclusive. Find the exact probability that the number selected is less than 100 or greater than 900. Answer. 19,9%.

EXERCISE 12. A labor study involves a sample of 12 mining companies, 18 construction companies, 10 manufacturing companies and 2 wholesale companies. If a company is randomly selected from this sample group, find the probability of getting a mining or construction company. Answer. 61/366.

EXERCISE 13. Two cards are to be drawn without replacement from an ordinary deck of playing cards. What is the probability that both of the cards drawn are aces? Answer. 12/2652.

EXERCISE 14. Of all students attending a given college, 40% are males and 4% are males majoring in art. A student is to be selected at random. Given that the selected student is male, what is the probability that he is an art major? Answer. 10%

EXERCISE 15. Two cards are to be drawn without replacement from an ordinary deck of playing cards. What is the probability a) that the first card to be drawn is a queen and the second card is king? b) of drawing a combination of queen and king? c) that neither of the two cards will be queen? d) that neither of the two cards will be queen or a king? Answer. a) 16/2652. b)32/2352. c) 2256/2652. d) 1892/2652.

EXERCISE 16. Urn A contains 4 white and 3 red marbles, urn B contains 2 white and 5 red marbles. A marble is to be selected from urn A and another marble is to be selected from urn B. What is the probability that the two marbles selected are white? Answer. 8/49.

Please show your workings. I have shown the possible answer already. Thank you!

Question 35

I) Suppose that you randomly select a sample of 40 part-time journalists in January, and find that the sample pay per hour is £20.10 and the sample SD is £3.15. Compute a 95% confidence interval for the mean hourly pay of all of the part-time journalists in January, and then provide an interpretation of your interval.


II) Suppose that part-time journalists earn £17.84 per hour on average in July. Test if the data collected in Part I) suggest that the part-time journalists in January earn, on average, more than those working as part-time journalists in July. Do a hypothesis test given a 10% significance level to answer this, and then provide a conclusion.

A company has 4 zones(north, south, east, west) and 4 supervisors available for assignment. It is estimated that a typical supervisor operating in each zone would bring in the following annual turnover: north:126000, south 105000, east 84000, west 63000. The 4 supervisors are also considered to differ in supervisory competencies. It is estimated that working under the same conditions, the company's yearly turnover would be proportionately as follows: supervisor I:7, supervisor II: 5, supervisor III:5, supervisor IV: 4. How should be the company allocate the best supervisor to the various zones in order to maximize its annual turnover. Use Hungarian method.

On May 3, 2017, the Calgary Herald reported that, according to Avalanche Canada, 24 of 45 people killed in avalanches over the previous 5 years were snowmobilers. Assume this is a random sample. a) Is the sample large enough that we can use techniques based on the normal distribution to analyze these data? Please explain. b) Calculate a 95% confidence interval for the proportion of avalanche deaths that are snowmobilers. c) Would a 99% confidence interval be wider or narrower? d) The claim is made that no more than 30% of all avalanche deaths are snowmobilers. What would the null and alternative hypotheses be if you want to show that the proportion is higher than 30% e) Based on your confidence interval, do you believe that more than 30% of all avalanche deaths are snowmobilers? Please explain.

Consider the following table:

Step 1 of 8:

Calculate the sum of squares of experimental error. Please round your answer to two decimal places.

Step 2 of 8:

Calculate the degrees of freedom among treatments.

Step 3 of 8:

Calculate the degrees of freedom of experimental error.

Step 4 of 8:

Calculate the mean square of the experimental error. Please round your answer to two decimal places.

Step 5 of 8:

What is the sum of squares of sample means about the grand mean? Please round your answer to two decimal places

Step 6 of 8:

What is the variation of the individual measurements about their respective means? Please round your answer to two decimal places.

Step 7 of 8:

What is the critical value of F at the 0.050.05 level? Please round your answer to four decimal places, if necessary.

Step 8 of 8:

Is F significant at 0.050.05?

1.

A random sample of fifteen male test scores resulted in a standard deviation of 4.2. A random sample of 20 female scores resulted in a standard deviation of 3.7. Is the variation in the male population more than that of the female population? a=0.05

What is the consequence of increasing the confidence in our interval estimate?

A sample of size 20 yields a sample mean of 23.5 and a sample standard deviation of 4.3.

Test HO: Mean >_ 25 at alpha = 0.10. HA: Mean < 25. This is a one-tailed test with lower reject region bounded by a negative critical value.

The average time spent sleeping (in hours) for a group of healthy adults can be approximated by a normal distribution with a mean of 6.5 hours and a standard deviation of 1 hour. Between what two values does the middle 70% of the sleep times lie?

Run a regression analysis on the following data set, where y is the final grade in a math class and x is the average number of hours the student spent working on math each week.

State the regression equation y = m ⋅ x + b, with constants accurate to two decimal places.

What is the predicted value for the final grade when a student spends an average of 9 hours each week on math? Grade = Round to 1 decimal place.