(a). (10 points) Is there sufficient evidence to indicate that our percentages of the colors for compact/sports cars differ from those given? Find the approximate p-value for the test (HINT: Remember to include a column called "Other" for cars that do not fall into one of the six categories shown in the table).

1. (10 points in total) The scores of English in a class are normally distributed. The distribution is divided into three portions, 5% of the students' scores are below 60 and 10% are above 80. Try to find the mean and the standard deviation for this course.

(a). (5 points) State the null and alternative hypothesis (H0 and H1). What statistic should be constructed for testing the hypothesis and explain why (t or Z statistic?)

(b). (5 points) Do you reject H0at the 5% level?

(a). (10 points) Do the data provide sufficient evidence to contradict the manufacturer's claim? (HINT: To be generous, let a range of 2% equal 4σ.)

(b). (5 points) Find a 90% confidence interval for σ²

(c). (5 points) What assumptions are made when you choose a test statistic for the hypothesis test above? Explain.

(b). (10 points) The researcher wants to see if there is a difference in the color distributions for compact/sports cars versus full/intermediate cars. Another random sample of 250 full/intermediate cars was taken and the color of the vehicles was recorded. The table below shows the results for both compact/sports and full/intermediate cars. Do the data indicate that there is a difference in the color distributions depending on the type of vehicle? Use α=0.05. 

(a). (15 points) Please construct an ANOVA table to test whether the data present sufficient evidence to indicate that the number of errors is related to the number of hours without sleep? What is the p-value?

(b). (10 points) Please construct a simple linear regression to test whether the data present sufficient evidence to indicate that the number of errors is related to the number of hours without sleep. What is the least-squares prediction equation? y = a + βx + ε

(c). (10 points) What is the sampling distribution on β? (Hint: probability distribution, mean, and standard error)

113年 - 113 國立臺灣大學_碩士班招生考試：工程統計#119664

112年 - 112 國立臺灣大學_碩士班招生考試試題：工程統計#119662

111年 - 111 國立臺灣科技大學_碩士班招生試題：統計學(C)#120895

110年 - 110 國立陽明交通大學_碩士班考試入學試題：統計學#121574

110年 - 110 國立臺灣科技大學_碩士班招生試題_企業管理系：統計學#111322

110年 - 110 國立臺灣大學_碩士班招生考試_部分系所:統計學(H)#111297

110年 - 110 國立政治大學_碩士班暨碩士在職專班招生考試_財政所:統計學#110890

110年 - 110 國立高雄科技大學_碩士班招生考試_工業工程與管理系：統計學#110420

110年 - 110 國立政治大學_碩士班招生考試_財政研究所:統計學#107983

110年 - 110 國立政治大學_碩士班招生考試_ 國際經營與貿易學系:統計學#106074