Question

It is claimed that the mean viscosity of product 2 is less than the mean viscosity of product 1. To test this claim 18 samples are taken from each products and average viscosities are measured as 10.57 and 10.51. It is known that the standard deviation of both products are 0.1. If you test the claim at 0.05 what would be the test statistics.

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The length of a day (X) and the electricity usage(Y) for that day recorded. Measuremenst for five days are given in the table below. Calculate the correlation of X and Y.

You want to test whether the correlation is different than 0 or not at 5%significance. If you perform correlation test, what would be your calculated t-test statistics?

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An automobile manufacturer claims that the variance of the fuel consumption for its hybrid vehicles is more than the variance of the fuel consumption for the hybrid vehicles of a top competitor. A random sample of the fuel consumption of 10 of the manufacturer's hybrids has a variance of 0.77. A random sample of the fuel consumption of 14 of its competitor's hybrids has a variance of 0.24. At α= 0.05 you would like to test claim. What will be your calculated test statistics?

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Three washing machines are being compared. They have been used multiple times to clean different dirty cloth piles. Their effectiveness are measured and scaled from 0..100. Then One way ANOVA test performed. The ANOVA table is given below. After finding the values for (*), What would be the estimate for the standard deviation of measurement errors?

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In an analysis of variance (ANOVA) problem involving 3 groups and 10 observations per group, SSE = 399.6. The MSE for this situation is

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An automobile manufacturer claims that the fuel consumption for its hybrid vehicles is uniformly distributed between 50 mpg and 60 mpg. A random sample of the manufacturer's hybrids (40 cars) are taken and the fuel consumptions are measured. 16 of the vehicles had fuel consumption between 50-54 mpg, 8 of them had between 54-56, 14 of them had between 56-58 and 12 of them had between 58-60 mpg. We test the claim at α =0.05.

We found that test statistic is less than table value. What does that mean

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An automobile manufacturer claims that the fuel consumption for its hybrid vehicles is uniformly distributed between 50 mpg and 60 mpg. A random sample of the manufacturer's hybrids (40 cars) are taken and the fuel consumptions are measured. 16 of the vehicles had fuel consumption between 50-54 mpg, 8 of them had between 54-56, 14 of them had between 56-58 and 12 of them had between 58-60 mpg. We test the claim at α =0.05.

We found that test statistic is less than table value. What does that mean

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An automobile manufacturer claims that the variance of the fuel consumption for its hybrid vehicles is more than the variance of the fuel consumption for the hybrid vehicles of a top competitor. A random sample of the fuel consumption of 10 of the manufacturer's hybrids has a variance of 0.77. A random sample of the fuel consumption of 14 of its competitor's hybrids has a variance of 0.24. At α= 0.05 you would like to test claim. Therefore what is your table value?

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An automobile manufacturer claims that the fuel consumption for its hybrid vehicles is uniformly distributed between 50 mpg and 60 mpg. A random sample of the manufacturerâ s hybrids are taken and the fuel consumptions are measured. 16 of the vehicles had fuel consumption between 50-54 mpg, 8 of them had between 54-56, 14 of them had between 56-58 and 12 of them had between 58-60 mpg. If we want to test the claim at ï ¡=0.05 what would be critical value?

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An engineer want to compare the performance of two machines.

Machine one produced average of 15 pcs/day in 10 days.

Machine two produced on the average 17 pcs/day in 12 days.

We know the standard deviations of these machines.The standard deviations are 2 pcs/day and 2.3 pcs/day respectively.

At %4 significance level, to test whether their means are equal or not; which test should engineer use?
The mean deflection temperature under load for two different types of plastic pipe is being investigated. Two random samples of 4 pipe specimens are tested, and the deflection temperatures observed are as follows (in °C):

Type 1

97

87

98

90

Type 2

80

92

95

93

We want to test the claim that the deflection temperature under load for type 1 pipe exceeds that of type 2!

So What would be the correct hypothesis?

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You analyze Covid-19 deaths. You want to test whether the death ratios for pre-existing medical conditions are affected by gender. The collected data is given in a table. If you want to test dependency at 10% significance what would be critical (table) value?

Pre-exixting Conditions

Male

Female

Cardiovascular disease

18

12

Diabetes

14

6

Chronic respiratory disease

8

7

Hypertension

10

5

Cancer

14

6

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Three washing machines are being compared. They have been used multiple times to clean different dirty cloth piles. Their effectiveness are measured and scaled from 0..100. Then One way ANOVA test performed. The ANOVA table is given below. After finding the values for (*), What would be the Mean Square Error for errors?

ANOVA

            
Sources

SS

Df

MS

F

Between

*

*

4

*

Within group

*

6

*

               
Total

16

8

Answer 1

question 1

Given mean of product 2 is less than mean of product 1

The test hypothesis is


Now, the value of test static can be found out by following formula:

Using Excel's function , the P-value for in an power-tailed t-test with 34 degrees of freedom can be computed as .
Since , we fail to reject the null hypothesis

Degrees of freedom on the t-test statistic are
n1 + n2 - 2 = 18 + 18 - 2 = 34

This implies that

Since, the t distribution is symmetric about zero, so
Since, we fail to reject the null hypothesis .