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Mathematics homework help

1.- The pulse rate of a man due to the effect of Amtas AT 25 mg on different days in a month were found to be.
66, 65, 69, 70, 69, 71, 70, 63, 64 and 68.
Discuss whether the mean pulse rate of the man in the month is 65. Assume significance level is 0.05.

  • State Null and Alternative hypotheses (3 points):
  • Compute Test Statistic (3 points):
  • Compute critical value or pvalue (3 points):
  • Decision and conclusion in terms of the problem (4 points):

2.Compute and interpret a 95% confidence interval for the mean pulse rate of subjects from problem 1.

  • Compute confidence interval (4 points):
  • Interpret confidence interval (4 points):

3.- In an experiment to investigate the possible protective effects of vitamin C against rabies 98 guinea-pigs were given a small dose of fixed rabies virus. Of these, 48 were also given vitamin C, the rest were not. Table 1 gives the number that died or survived under each treatment. Deaths occurred in 35% of the treated and 70% of the control animals. Carry out a test with Yate’s correction to decide if vitamin C is effective against rabies.
Table 1.

Treatment No. of deaths No. of survivors
Vitamin C 17 31
Control 35 15
  • State Null and Alternative hypotheses (3 points):
  • Compute Test Statistic (3 points):
  • Compute critical value or pvalue (3 points):
  • Decision and conclusion in terms of the problem (4 points):
  1. The scutum widths of ticks collected from three cotton-tail rabbits were measured and the data are given in Table 2. Using Satterthwaite’s rule to determine the appropriate number of degrees of freedom (unequal variance), carry out t tests to decide which, if any, of the mean scutum widths differ significantly. Make the comparisons with Bonferroni’s correction and without a correction for the number of comparisons.

Table 2. Number of ticks, mean scutum width in microns and standard deviation of the mean width in microns, taken from each of three rabbits

Rabbit n m sd
1 8 372.3 6.23
2 10 354.4 2.60
3 13 355.3 3.77

For each comparison state: – State Null and Alternative hypotheses (4 points):

  • Compute Test Statistic (5 points):
  • Compute critical value or pvalue (with and without correction) (6 points):
  • Decision and conclusion in terms of the problem (with and without correction) (6 points):

5.- We want to compare the effect on sleep of two different drugs (hyoscyamine and Hyoscine) on patients. How many patients would you need to use in order to decide if hyoscyamine increases the amount of sleep by at least 30 minutes while keeping the probability of making a Type I error to less than 5% and the probability of making a Type II error to less than 10% (=0.9)? From a pilot sample we have, sd hyoscyamine=1.79 and sd Hyoscine=2.
Write the correct formula to use (3 points):
Write formula with values plugged in (3 points):
Sample size needed per group (3 points):
6.- An experiment was performed in which tick larvae of the species Haemaphysalis leporispalustris were collected from four cotton-tail rabbits.
 
Table 3 Scutum widths, cottontail rabbits in microns, of tick larvae taken from four Rabbits.

  1 2 3 4
  380 350 354 376
  376 356 360 344
  360 358 362 342
  368 376 352 372
  372 338 366 374
  366 342 372 360
  374 366 362  
  382 350 344  
  344 342    
  364 358    
  351      
  348      
  348      
m 372.3 354.4 355.3 361.3
sd 6.23 2.60 3.77 2.47

Carry out a one way ANOVA test.

  • State Null and Alternative hypotheses (3 points):
  • Calculate the ANOVA table (4 points):
  • Compute pvalue (3 points):
  • Decision and conclusion in terms of the problem (4 points):

7.- We consider an experiment of the diet of rats where we examined the extent to which the freshness of the lard and the sex of the rats affected the weight gained by the rats. Table 4 The weight (in grams) gained by male rats fed on fresh lard and on rancid lard , and by female rats fed on fresh lard and on rancid lard.
Table 4.

  A1 ( fresh lard) A2 (rancid lard)
  171 108
B1 (male rats) 172 89
  172 69
     
  153 85
B2 (female rats) 109 64
  160 82

Carry out a two way ANOVA test.

  • Calculate the ANOVA table (5 points):
  • Compute pvalues for overall effect, sex effect, diet effect and interaction effect (6 points):
  • Decision and conclusion in terms of the problem for each one of the tests (6 points):

8.- Find the correlation coefficient and the equation of the regression line of the following values of x and y.
{(x,y)}={(1,2),(2,5),(3,3),(5,8),(5,7)}

  • Correlation coefficient (4 points):
  • Regression line (4 points):

 

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