Question

Last year, 40.9 % of all US auto sales were Japanese models. A random sample of 379 auto sales this year was obtained to determine if a greater percentage is from Japanese models this year. Among the auto sales, there were 183 that were Japanese models. Test the appropriate hypotheses using a significance level of 0.10.

• H0:H0: Select an answer p̂ p  ? = > < ≠     Ha:Ha: Select an answer p p̂  ? > < ≠  
• αα =    decision rule: reject H0H0 if probability ? < ≠ >  αα  
• Test Statistic: z =   (Note: round the z-score to two decimal places - carry at least four decimal places throughout all of your calculations)
• probability =   (Note: round the probability to four decimal places)
• decision: Select an answer Reject H₀ Do NOT reject H₀
• Conclusion: At the 0.10 level, there Select an answer is is not  significant evidence to conclude the percentage of US auto sales that are Japanese models this year is Select an answer greater than less than different than  than 40.9%.

Answer 1

Ho: p = 40.9%
h1: p > 40.9%

a = 10%

decision rule:
reject H0 if probability < α

p-hat = X/n = 183/379 = 0.483

test statistic:
z = (phat-p)/sqrt(p*(1-p)/n)
z = (0.483-0.409)/SQRT(0.409*(1-0.409)/379)
z = 2.930

probability =
p-value
= 1-P(Z<z)
= 1-P(z<2.930191)
= 1-NORMSDIST(2.930191)
= 0.0017

decision:
Since p<10%, i Reject H₀

Conclusion:
At the 0.10 level, there is significant evidence to conclude the percentage of US auto sales that are Japanese models this year is greater than 40.9%.