Question

In: Statistics and Probability

The survival times in weeks for 20 male rats that were exposed to a high level...

The survival times in weeks for 20 male rats that were exposed to a high level of radiation are152 152 115 109 137 88 94 77 160 165 125 40 128 123 136 101 62 153 83 69. Data are from Lawless (1982) and are stored in the data frame RAT. Load the data with data(RAT)Construct a 95% confidence interval for the average survival time for male rats exposed to high levels of radiation. Round to two decimal places.

Hint: Use T-distribution as sample is small and variance unknown.

CI <- t.test(RAT$survival.time, conf.level = ???)$conf

Expert Solution

Solution:

x	x²
152	23104
152	23104
115	13225
109	11881
137	18769
88	7744
94	8836
77	5929
160	25600
165	27225
125	15625
40	1600
128	16384
123	15129
136	18496
101	10201
62	3844
153	23409
83	6889
69	4761
x=2269	x²=281755

The sample mean is

Mean = (x / n) )

=152+152+115+109+137+88+94+77+160+165+125+40+128+123+136+101+62+153+83+69/20

=2269 /20

=113.45

Mean =113.45

The sample standard is S

S =( x² ) - (( x)² / n ) n -1

=(281755-(2269)²20 /19 )

=(281755-257418.05 /19)

=24336.95/19

=1280.8921

=35.789

The sample standard is = 35.79

Degrees of freedom = df = n - 1 = 20 - 1 = 19

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

t_/2,df = t_0.025,19 =2.093

Margin of error = E = t_/2,df * (s / $\sqrt$ n)

= 2.093 * (35.79 / $\sqrt$ 20)

= 16.75

Margin of error =16.75

The 95% confidence interval estimate of the population mean is,

- E < < + E

113.45 - 16.75 < < 113.45 + 16.75

96.70 < < 130.20

(96.70, 130.20 )

orchestra answered 2 years ago

Different breeding lines of rats ran a maze, then were exposed to an EMP (electro magnetic...

Different breeding lines of rats ran a maze, then were exposed to an EMP (electro magnetic pulse, such as would occur from a nuclear explosion then ran a similar maze again. The maze running times were compared and the rats were classified into 3 groups. After slower than before, after close to before, and after faster than before. The categories are shown in the table below. Are different broads reacting differently to radiation? Test at the .01 level. Breeding line...

Male and female Rats (sex) were provided with either food of type 1 or food of...

Male and female Rats (sex) were provided with either food of type 1 or food of type 2 (food) and the subsequent consumption (cons) rate was measured. Was there a difference in the consumption rate of rats based on the food type and their sex? Use the data provided on Blackboard (‘RatsFood.xlsx’to complete the analysis as asked below). For this question – the data are indeed normally distributed (no need to check)… What are the null and alternative hypotheses? What...

Here are the survival times in days of 72 guinea pigs after they were injected with...

Here are the survival times in days of 72 guinea pigs after they were injected with infections bacteria in a medical experiment. Survival times, whether of machines under stress or cancer patients after treatment, usually have distributions that are skewed to the right. 43 45 53 56 56 57 58 66 67 73 74 79 80 80 81 81 81 82 83 83 84 88 89 91 91 92 92 97 99 99 100 100 101 102 102 102 103...

The survival times in days of 72 guinea pigs after they were injected with infectious bacteria...

The survival times in days of 72 guinea pigs after they were injected with infectious bacteria in a medical experiment is displayed in the table. 43 45 53 56 56 57 58 66 67 73 74 79 80 80 81 81 81 82 83 83 84 88 89 91 91 92 92 97 99 99 100 100 101 102 102 102 103 104 107 108 109 113 114 118 121 123 126 128 137 138 139 144 145 147 156...

At a western hospital, there were a total of 932 births in 20 consecutive weeks. Of...

At a western hospital, there were a total of 932 births in 20 consecutive weeks. Of these births, 216 occurred on weekends. Based on these data, are births rates different on weekends compared to weekdays? Use a chi-square test. I have already done the chi-square test with 1 proportion. The question I need help with is listing 2 other statistical tests that can be used to test the hypothesis and what the advantages/disadvantages are.

1. Twenty male athletes were given a special candy bar daily for several weeks, and each...

1. Twenty male athletes were given a special candy bar daily for several weeks, and each man’s body weight was recorded. It is found that the mean change in body weight was +1.5 kg. The variance of these 20 data of weight-change has been estimated as s2 = 6.25 kg2. (50 pts) – t distribution and chi-square distribution tables are included. (a) Test the null hypothesis that the candy bar has NO significant effect on body weight. (b) Test the...

A summer camp hired 20 counselors for the summer. Ten were male and ten were female....

A summer camp hired 20 counselors for the summer. Ten were male and ten were female. There is a concern that the males were paid more for the summer work than the females. To investigate this concern, males and females were paired based on their experience. Pair Male Female 1 14,300 13,800 2 16,500 16,600 3 15,400 14,800 4 13,500 13,500 5 18,500 17,600 6 12,800 13,000 7 14,500 14,200 8 16,200 15,100 9 13,400 13,200 10 14,200 13,500 Calculate...

1. A 20 year old male complains of sudden onset shortness of breath at 24 times...

1. A 20 year old male complains of sudden onset shortness of breath at 24 times per minute and his pulse aximetry is 85% aCoach him on slowing his rate of respiration bApply oxygen via nasal cannula at 4lpm - correct cAdminister oxygen via nonrebreather mask at 15lmp dVentilate the patient at a rate of 12 breaths per minute 2.A thin 75 year old male complains of difficulty breathing. He states he has smoked "3 packs of cigarettes a day...

The data below were obtained to predict the sound frequency to which a person’s ear will respond based upon the length of time a person has been exposed to a high level of noise.

The data below were obtained to predict the sound frequency to which a person’s ear will respond based upon the length of time a person has been exposed to a high level of noise. Here “length of exposure” is the amount of time in weeks that a person has been living close to a major airport and the “hearing range” is reported in thousand cycles per second. Length of exposure In weeks (Left) Hearing range In thousand cycles per second...

In a Survey people were asked to report their level of Math Anxiety as High, Medium,...

In a Survey people were asked to report their level of Math Anxiety as High, Medium, Low or None. The table below reflects the results. The question is: Is there evidence that the level of math anxiety is different for female and male students at the α = 0.1 level of significance? Perform a Test for Homogeneity of Proportions. High/Medium Low/None Female 19 9 Male 12 8