Question

please show steps for both Q8 and Q9

QUESTION 8 A company that produces light bulbs wants to test in their new LCD bulb has an average lifespan that exceeds 5000 hours. To support their claim they have collected a random sample of 91 bulbs and found the average lifespan of these 91 bulbs was 5,168 hours. The population standard deviation is known to be 457 hours. The company would like to test their hypothesis using a significance level of 0.05. Calculate the appropriate test statistic. QUESTION 9 A simple linear regression has been performed to estimate the relationship between fuel efficiency in miles per gallon) and engine size (in cubic liters). The regression results are displayed in the following table: SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations 0.8399 0.7055 0.6564 1.8203 ANOVA dy F 14.3706 Significance 0.0091 Regression Residual Total MS 47.6184 3.3136 1 6 7 SS 47.6184 19.8816 67.5 Intercept Engine Size Coefficients 37.4528 -4.6119 Standard Error 3.1535 1 2166 Stat 11.8766 -3.7909 P-value 0.0000 0.0091 Lower 95% 29.7365 -7.5889 Upper 95% 45.1691 -1.6350 What is the predicted value of fuel efficiency (in miles per gallon) for a car with a 2.5 cubic liters engine? Round your answer to two decimals, if needed.

Answer 1

Question 8:

The test statistic is Z=3.5068

Decision: Reject the Null hypothesis and conclude that there is enough evidence to claim that the average lifespan exceeds 5000 hours.

Question 9:

The predicted value of fuel efficiency for a car with 2.5 liters engine=25.92 mpg.

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We are given that n=91, $\sigma=457,\bar{x}=5168$ . Since the population sd is known, we shall apply Z test for testing:

H:= 5000

$H_{1}:\mu>5000$

Test statistic: will have a Standard Normal distribution.

I N - g/n

The critical region: $R=\left \{ z:z>1.6449 \right \}$

$Z=\frac{5168-5000}{547/\sqrt{91}}$

$Z=\frac{168}{547/9.5394}$

$Z=\frac{168}{47.9066}$

$Z=3.5068$

Question 9:

The estimated regression equation is fuel efficiency=37.4528-4.6119*engine size

For a 2.5 litre capacity, the fuel efficiency is fuel efficiency=37.4528-4.6119*2.5=37.4528-11.52975=25.92305 m[pg