You wish to test the claim μ<68.5μ<68.5 at a significance level of 0.100.10. You believe the population is normally distributed, but you do not know the standard deviation. You obtain the following sample of data: data 67.7 42.1 94.4 67.2 16.9 49.7 30.2 65.2
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You wish to test the claim μ<68.5μ<68.5 at a significance level of 0.100.10.
You believe the population is
| data |
|---|
| 67.7 |
| 42.1 |
| 94.4 |
| 67.2 |
| 16.9 |
| 49.7 |
| 30.2 |
| 65.2 |
What is the critical value for this test? (Report answer accurate to three decimal places.)
critical value =
What is the test statistic for this sample? (Report answer accurate to three decimal places.)
test statistic =
Claim:
μ<68.5
Null Hypothesis:
H0:
Alternative Hypothesis:
H0:
Critical value:
degrees of freedom=n-1=8-1=7
level of significance=0.10
Tail of the test is left tail test.
t critical value=-1.415, from the excel function, =T.INV(0.1,7)
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- The average speed of 100 random cars traveling on a certain highway was 80 km/h. From past information, we can assume that the standard deviation of the population is 20 km/h. What is the margin of error with a 99% level of confidence for the population average ?speed :Select one a. 5.152 O b. 2.326 O c. 2.564 O d. 1.282 O e. 2.576 O f. 4.652 OYou wish to test the following claim (Ha) at a significance level of a = 0.01. Ho: H 63.6 На: и > 63.6 You believe the population is normally distributed, but you do not know the standard deviation. You obtain the following sample of data: data 66.9 78.6 53.8 57.9 57 What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic = What is the p-value for this sample? (Report answer accurate to four decimal places.) p-value =You wish to test the following claim (H₁) at a significance level of a = 0.05. Hou= 81.3 H₁ 81.3 You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n = 16 with mean = 87.2 and a standard deviation of s = 8.7. What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic = What is the p-value for this sample? (Report answer accurate to four decimal places.) p-value = The p-value is... Ꮕ less than (or equal to) a greater than a
- You wish to test the following claim (Ha) at a significance level of a = 0.01. H.:µ = 73.7 HaiH + 73.7 You believe the population is normally distributed, but you do not know the standard deviation. Your sample has: size: n = 54 mean: M = 65.8 standard deviation: SD = 20.1. What is the test statistic for this sample? (Round the answer accurate to 3 decimal places.) test statistic: t = What is the P-value for this sample? (Round the answer accurate to 3 decimal places.) P-value = The P-value is... less than (or equal to) a greater than a This leads to a decision to... reject the null accept the null fail to reject the null So, the final conclusion is that... The data do not support the claim of the alternative hypothesis that the population mean is not equal to 73.7. The sample data support the claim of the alternative hypothesis that the population mean is not equal to 73.7.This assignment is worth 1 points. The extra point will be added to your overall course grade. For example: if you receive an 88% in the course you can receive up to 1 point giving you a new score of 89%. The following rubric will be used. 0.25 point for drawing the normal distribution curve with the mean value labeled on the curve and the appropriate area shaded. 0.25 point for determining the value of the standard deviation of the sample mean. 0.5 point for finding the correct probability. All work must be shown in order to receive any credit. Please upload your completed assignment here. The length of time taken on the SAT for a group of students is normally distributed with a mean of 2.5 hours and a standard deviation of 0.25 hours. A sample size of n = 60 is drawn randomly from the population. Find the probability that the sample mean is between two hours and three hours.You wish to test the following claim (H.) at a significance level of a = 0.01. H.:µ = 75.8 Ha:µ > 75.8 You believe the population is normally distributed, but you do not know the standard deviation. Your sample has: size: n = 73 mean: M = 77.2 standard deviation: SD = 8.5. What is the test statistic for this sample? (Round the answer accurate to 3 decimal places.) test statistic: t = What is the P.value for this sample? (Round the answer accurate to 3 decimal places.) P-value = The P-value is... O less than (or equal to) a O greater than a This leads to a decision to... O reject the null O accept the null O fail to reject the null So, the final conclusion is that... O The data do not support the claim of the alternative hypothesis that the population mean is greater than 75.8. O The sample data support the claim of the alternative hypothesis that the population mean is greater than 75.8.
- You wish to test the following claim (Ha) at a significance level of a = 0.005. H,:µ = 90.6 Ha:µ < 90.6 You believe the population is normally distributed, but you do not know the standard deviation. You obtain the following sample of data: data 95.7 78.9 81.3 What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic = What is the p-value for this sample? (Report answer accurate to four decimal places.) p-value = The p-value is... Oless than (or equal to) a greater than aThe time to complete an exam is approximately Normal with a mean μ = 47 minutes and a standard deviation o = 8 minutes. The bell curve below represents the distribution for testing times. The scale on the horizontal axis is equal to the standard deviation. 1. Fill in the indicated boxes. μ-3σ μ-2ο μίσ + μ μ+o 47 minutes. 2. Used the Empirical Rule to complete the following statements: 95% of testing times were between and μ = 47 σ = 8 μ+20 μ+30 minutes and 55 minutes. minutes % of the testing times were between 39A survey found that the average hotel room rates and standard deviations for the state of Arkansas and the state of Washington. Assume that the data were obtained from two samples were normally distributed. At a=0.1 level of significance, can it be concluded that there is a significant difference in the rates? Use the data table below. Report only the value required from the question below make sure to express your final answers in 4 decimal places. Parameter Arkansas Washington Sample size 82.00 72.00 sample 350.46 360.01 mean population standard deviation 29.17 27.20 a. Variance of Arkansas:
- Apply the Empirical Rule to solve the following: The weight of a newborn manatee calf is normally distributed with a mean of 66 lbs and a standard deviation of 4 lbs. (Do NOT overuse the calculator on this problem. Apply the Empirical Rule.) a.Draw and label the normal curve. (Don’t forget the word label on the x-axis) b.What percent of manatee calves have a birth weight between 54 and 78 lbs? c. What percent of manatee calves have a birth weight of more than 74 lbs? d .What is the birth weight of the middle 68% of manatee calves? e. What percent of manatee calves weigh more than 58 lbs at birth? f. How much do the smallest 0.15% of manatee calves weigh at birth? g. What percent of manatee calves weigh less than 62 lbs at birth? h. What percent of manatee calves weigh 66 lbs or more at birth?You wish to test the following claim (Ha) at a significance level of a = 0.02. H.:µ = 73.5 Ha:µ + 73.5 You believe the population is normally distributed, but you do not know the standard deviation. Your sample has: size: n = 61 mean: M = 76 standard deviation: SD = 18.1. What is the test statistic for this sample? (Round the answer accurate to 3 decimal places.) test statistic: t = What is the P-value for this sample? (Round the answer accurate to 3 decimal places.) P-value = The P-value is... less than (or equal to) a greater than a This leads to a decision to... reject the null accept the null fail to reject the null So, the final conclusion is that... O The data do not support the claim of the alternative hypothesis that the population mean is not equal to 73.5. The sample data support the claim of the alternative hypothesis that the population mean is not equal to 73.5.You wish to test the following claim at a significance level of a=0.10. H0:U=81.8 H1:U<81.8You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size 90 with mean 77.6 and a standard deviation of 14.8.What is the test statistic for this sample? (Report answer accurate to 3 decimal places.)What is the p-value for this sample? (Report answer accurate to 4 decimal places.)This test statistic leads to a decision to reject the null accept the null fail to reject the null As such, the final conclusion is that there is sufficient evidence to conclude that the population mean is equal to 81.8. there is not sufficient evidence to conclude that the population mean is equal to 81.8. there is sufficient evidence to conclude that the population mean is less than 81.8. there is not sufficient evidence to conclude that the population mean is less than 81.8.
