Test of Hypothesis on the Population Means

A researcher reports that the average IQ level of students in Malinta Senior High School is 100. A sample of 20 students has a mean IQ level of 105 with a standard deviation of 8. In testing the claim that the IQ level of students is 100, at 5% level of significance, which of the following illustrates the correct null & alternative hypotheses?

• H_o: μ=100;

  H_a: μ<100

• H_o​: μ=100;

  H_a: μ>100

A researcher reports that the average IQ level of students in Malinta National Senior High School is 100. A sample of 20 students has a mean IQ level of 105 with a standard deviation of 8. In testing the claim that the IQ level of students in DORSHS is 100, at 5% level of significance, calculate the appropriate test statistic.

• z=−2.795

• t=2.795

• t=−2.795

• z=2.795

A researcher reports that the average IQ level of students in Malinta Senior High School is 100. A sample of 20 students has a mean IQ level of 105 with a standard deviation of 8. In testing the claim that the IQ level of students is 100, at 5% level of significance, what is the appropriate critical value of the rejection region for the given level of significance?

• ±2.086

• -2.093

• +2.093

• ±2.093

Answer explanation

since n=20 df=n-1=20-1 on a two tailed test with 5% level of significance

A researcher reports that the average IQ level of students in Malinta Senior High School is 100. A sample of 20 students has a mean IQ level of 105 with a standard deviation of 8. In testing the claim that the IQ level of students is 100, at 5% level of significance, what is the appropriate decision.

• Reject the Null Hypothesis

• Do not reject the Null Hypothesis

Answer explanation

since t=2.795 falls under rejection region

A researcher reports that the average IQ level of students in Malinta Senior High School is 100. A sample of 20 students has a mean IQ level of 105 with a standard deviation of 8. Test the claim that the IQ level of students is 100, at 5% level of significance. Choose the appropriate conclusion.

• There is sufficient evidence to reject the claim that the average IQ level of Malinta Senior High School is 100

• There is no sufficient evidence to reject the claim that average IQ level of Malinta Senior High School is 100

• There is sufficient evidence to reject the claim that the average IQ level of Malinta Senior High School is 105

• There is no sufficient evidence to reject the claim that average IQ level of Malinta Senior High School is 105

A drink vending machine is adjusted so that, on average, it dispenses 250ml of fruit juice with a standard deviation of 25ml into a plastic cup. However, the machine tends to go out of adjustment and periodic checks are made to determine the average amount of fruit juice being dispensed. The operator thinks that the amount dispensed is less than 250 ml. So to verify, a sample of 35 drinks is taken to test the adjustment of the machine and a mean of 225 is obtained. For α = 5%, what is the appropriate hypotheses?

• H_o​: The amount dispensed on a vending machine is 250mL.

   H_a: The amount dispensed on a vending machine is less than 250mL.

• H_o​: The amount dispensed on a vending machine is 250mL.

   H_a: The amount dispensed on a vending machine is not 250mL.

• H_o​: The amount dispensed on a vending machine is at most 250mL.

   H_a: The amount dispensed on a vending machine is greater than 250mL.

• H_o​: The amount dispensed on a vending machine is 250mL.

   H_a: The amount dispensed on a vending machine is greater than 250mL.

A drink vending machine is adjusted so that, on average, it dispenses 250ml of fruit juice with a standard deviation of 25ml into a plastic cup. However, the machine tends to go out of adjustment and periodic checks are made to determine the average amount of fruit juice being dispensed. The operator thinks that the amount dispensed is less than 250 ml. So to verify, a sample of 35 drinks is taken to test the adjustment of the machine and a mean of 225 is obtained. For α = 5%, calculate the appropriate test statistics. 

• t=−5.916

• t=5.916

• z=−5.916

• z=5.916

A drink vending machine is adjusted so that, on average, it dispenses 250ml of fruit juice with a standard deviation of 25ml into a plastic cup. However, the machine tends to go out of adjustment and periodic checks are made to determine the average amount of fruit juice being dispensed. The operator thinks that the amount dispensed is less than 250 ml. So to verify, a sample of 35 drinks is taken to test the adjustment of the machine and a mean of 225 is obtained. For α = 5%, determine the appropriate critical value.

• −2.042

• −1.697

• −1.96

• −1.645

Answer explanation

since this is a left tailed test at 5% level of significance therefore, z critical value is -1.645

A drink vending machine is adjusted so that, on average, it dispenses 250ml of fruit juice with a standard deviation of 25ml into a plastic cup. However, the machine tends to go out of adjustment and periodic checks are made to determine the average amount of fruit juice being dispensed. The operator thinks that the amount dispensed is less than 250 ml. So to verify, a sample of 35 drinks is taken to test the adjustment of the machine and a mean of 225 is obtained. For α = 5%, determine the appropriate decision.

• Reject the Null 

  Hypothesis

• Do not reject the Null Hypothesis

• Reject the 

  Alternative 

  Hypothesis

• Reject both null and alternative hypothesis

Answer explanation

since z value -5.916 is less than the critical value -1.645 therefore it lies on a rejection region

A drink vending machine is adjusted so that, on average, it dispenses 250ml of fruit juice with a standard deviation of 25ml into a plastic cup. However, the machine tends to go out of adjustment and periodic checks are made to determine the average amount of fruit juice being dispensed. The operator thinks that the amount dispensed is less than 250 ml. So to verify, a sample of 35 drinks is taken to test the adjustment of the machine and a mean of 225 is obtained. For α = 5%, choose the appropriate conclusion.

• There is no sufficient evidence to verify that the vending machine dispensed 250 mL

• There is sufficient evidence to verify that the vending machine dispensed less than 250 mL