hypothesis testing

Question

1.Out of 10000 pumkins harvested,1000 where randomly selected 8% where found to be rotten the grower claims that only 6% are rotten. Is  this claim tenable /accepted .test at 5% level of significance.

Answer 1

H0: p=0.06 (the growers’ claim)

Ha: p≠0.06

Type of test: proportion, 2-tailed

Significance: 5%=0.05, but this is split between the two tails: 0.025 for each tail corresponds to a Z-score of 1.96.

Test statistic for proportions: (0.8-0.6)/√(pq/1000), where q=1-p=0.94.

Z-score for the test statistic=0.2/0.00751=26.63. This is an extremely large value corresponding to a probability of almost zero. H0 is therefore rejected. We therefore state that the proportion is not 6%.