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Answer: (72.535, 76.665)
Step-by-step explanation:
The confidence interval for population mean is given by :-

, where
= population standard deviation.
n= Sample size
= sample mean.
= Critical z-value (two-tailed)
Given : 
n= 81

The critical values for 90% confidence interval : 
Now, the confidence interval for population mean would be :

Hence, a 90 percent confidence interval estimatefor the average score of all students. : (72.535, 76.665)
Answer:
The observed value of the chi-square statistic is 34.71
Step-by-step explanation:
Given the data in the question';
Calculate the observed value of the chi-square statistic
The chi-square statistic will be;
∑
[ ( O
- E
)² / E
]
here O
is observed frequency of
th class
E
is expected frequency of
th class
= 1, 2 which denote the class of food experts who guess correctly and who didn't guess correctly
so
∈
= n × probability of not guessing correctly = 168 × 2/3 = 112
∈1 = n × probability of guessing correctly 168 × 1/3 = 56
so
∑
[ ( O
- E
)² / E
] = [ ( 92 - 56)² / 56 ] + [ ( 76 - 112)² / 112 ]
= 1296/56 + 1296/112
= 23.14 + 11.57
= 34.71
Therefore, the observed value of the chi-square statistic is 34.71
Answer:
x = 4, 3/2
Step-by-step explanation: