The people’s weights are normally distributed with a mean . On the other hand, the standard deviation is . Given that 15 people have a weight of 1200kg (average of 80kg person), we need to determine the probability;
The z-score is;
The probability is 0.1966.
The hypothesized proportion is . The sample size is and the number of favorable cases (number of customers who prefer the new brand) is . Therefore, the proportion of customers who prefer the new brand is;
The objective is to investigate whether at least 75% of users prefer the new brand.
The hypotheses are;
The test is equivalent to a right-tailed test, for which a z-test for one population proportion is used.
The significance level is . Therefore, the critical value is;
Thus, the rejection region is .
The test statistic is given by;
Since the test statistic , the null hypothesis is not rejected. It is concluded that there is not enough evidence to claim that at least 75% of users prefer the new brand.
The random sample of the visitors to the exhibition is . The sample mean of the amount spent is and the sample standard deviation is .
The sample size is . Thus, the number of the degrees of freedom is;
The significance level is . Therefore, the two-tailed critical value is;
The 95% confidence interval is given by;
The confidence interval is .
The significance level is and the number of degrees of freedom is . Therefore, the critical value is;
The rejection region is
The test statistic is given by;
Since the absolute test statistic , the null hypothesis is not rejected. It is concluded that there is not enough evidence to claim that the population mean is significantly different from $75.
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