Question

The US Department of Energy reported that 46% of homes were heated by natural gas. A random sample of 300 homes in Oregon found that 138 were heated by natural gas. Test the claim that proportion of homes in Oregon that were heated by natural gas is different than what was reported. Use a 1% significance level. Give answer to at least 4 decimal places.

What are the correct hypotheses? (Select the correct symbols and use decimal values not percentages.)

H₀: Select an answer σ p σ² s² x̄ p̂ μ s  ? < > = ≤ ≥ ≠   

H₁: Select an answer s σ x̄ μ σ² s² p̂ p  ? ≤ > < ≥ ≠ =   

Based on the hypotheses, find the following:

Test Statistic =  

p-value =

Based on the above we choose to Select an answer Reject the null hypothesis Accept the alternative hypotheis Accept the null hypothesis Fail to reject the null hypothesis

The correct summary would be: Select an answer There is not enough evidence to support the claim There is not enough evidence to reject the claim There is enough evidence to reject the claim There is enough evidence to support the claim  that the proportion of homes in Oregon that were heated by natural gas is different than what the DOE reported value of 46%.

Test the claim that the proportion of men who own cats is significantly different than the proportion of women who own cats at the 0.05 significance level.

The null and alternative hypothesis would be:

• Ho:pM=pFHo:pM=pF
  Ha:pM≠pFHa:pM≠pF
• Ho:μM=μFHo:μM=μF
  Ha:μM<μFHa:μM<μF
• Ho:μM=μFHo:μM=μF
  Ha:μM≠μFHa:μM≠μF
• Ho:pM=pFHo:pM=pF
  Ha:pM<pFHa:pM<pF
• Ho:μM=μFHo:μM=μF
  Ha:μM>μFHa:μM>μF
• Ho:pM=pFHo:pM=pF
  Ha:pM>pFHa:pM>pF

The test is:

• two-tailed
• right-tailed
• left-tailed

Based on a sample of 40 men, 40% owned cats
Based on a sample of 20 women, 60% owned cats

The test statistic is: z =  (to 2 decimals)

The P-value is:  (to 2 decimals)

Based on this we:

• Fail to reject the null hypothesis
• Reject the null hypothesis

Answer 1

( 1 )

Test Statistics

Test Statistics = 0

p value = 1

Conclusion

There is not enough evidence to support the claim that proportion of homes in Oregon that were heated by natural gas is different than what the DOE reported value of 46%.