Test of Hypothesis on Population Proportion

It has been claimed that 40% of students in a particular senior high school dislike Mathematics. When a survey was conducted by a researcher, it showed that 145 of 800 students dislike Mathematics. Test if the claim was different at α = 0.05 level. What is the appropriate alternative hypothesis?

• $p=0.40$
  

• $p\ne0.40$
  

• $p<0.40$

• $p>0.40$

A survey conducted last year by certain barangay officials showed that 40% of the residents owned a private car. This year a new survey is conducted on 375 residents selected randomly from the same barangay. It was found out that 190 of them own a car. Test if the claim is fewer at α = 0.01 level. Formulate the appropriate null hypothesis.

•  $H_a:\ p\ =0.40$ 
  

•  $H_o:\ p=0.40$ 
  

•  $H_o:\ p<0.40$ 

•  $H_a:\ p>0.40$ 

A survey conducted last year by certain barangay officials showed that 40% of the residents owned a private car. This year a new survey is conducted on 375 residents selected randomly from the same barangay. It was found out that 190 of them own a car. Test if the claim is fewer at α = 0.01 level. What is the correct alternative hypothesis in sentence form?

• The proportion of residents who owned a private car is 40%. 
  

• The proportion of residents who owned a private car is higher than 40%.
  

• The proportion of residents who owned a private car has changed to 40%.
  

• The proportion of residents who owned a private car is fewer than 40%. 
  

In a certain senior high school, a study found that 972 out that 1,100 Grade 12 students use smartphones. Using α = 0.10 level, is there enough evidence to conclude that the percentage of students who are using smartphones is different from 25%? What is the appropriate alternative hypothesis? 

• Ha: p > .25
  

• Ha: p = .25
  

• Ha: p < .25
  

• Ha: p ≠ .25
  

In a certain senior high school, a study found that 972 out that 1,100 Grade 12 students use smartphones. Using α = 0.10 level, is there enough evidence to conclude that the percentage of students who are using smartphones is different from 25%? What type of test is used?

• left-tailed
  

• non-directional
  

• right-tailed
  

• one directional
  

What is the sample proportion if n = 740 and x = 259? 

• 0.35
  

• 0.50
  

• 0.56
  

• 0.65
  

Tags

CCSS.HSS.IC.B.4

In a study about household income conducted in a small town, it was found out that 7% of all families in the town earn less than P4,000 per month. Out of 64 families who were randomly selected, 10 families earn less than P4,000 per month. Is the sample large enough to use the Central Limit Theorem? A.  C.  B.  D. 

• No, because 10/64 <5

• No, because 64(0.07)<5
  

• Yes, because 64>30
  

• Yes, because 64(0.93)>5
  

Tags

CCSS.HSS.ID.A.4

An insurance company reported that 30% of those persons involved in minor traffic accidents this year have been involved in at least one traffic accident in the last three years. Believing it was too large, an advisory group decided to investigate this claim. A sample of 200 traffic accidents this year showed that 56 persons were also involved in another accident in the last three years. Determine the value of the population proportion. 

• 0.28

• 0.30
  

• 3.57
  

• 0.60
  

Tags

CCSS.HSS.IC.B.4

Which of the following test statistic is appropriate to use in testing hypothesis involving population proportion? 

• t-test

• z-test
  

• p-test

• chi-square
  

Which of the following situations is directional? 

• A teacher wants to know if listening to popular music affects the performance of the pupils. 
  

• The principal claims that more than 30% of Grade 4 students are in favor of staying in the playground after classes. 
  

• The owner of a factory that sells a particular bottled juice drink claims that the content of his product is 250ml. 
  

• There is enough evidence to conclude that the percentage of students who are in favor of the new uniform is different from 85%.