Suppose that the bollywood movie industry wants to know how often college students go to the movies. Sixteen college students are selected at random from a city and asked how many movies they have seen in theater in the previous year. The data are as follows: 7, 13, 0, 10, 2, 8, 4, 11, 0, 5, 16, 6, 2, 12, 9, 0. Suppose that the national average for movie visits per person in a year is 9.0 and standard deviation is 4.0. a. State the NULL and Alternative hypothesis.b. Test statistically whether college students' habit of watching movie in theatre is significantly different from the population? The 95% region of acceptance for the test-statistic is [-1.96 : 1.96].
Question
Suppose that the bollywood movie industry wants to know how often college students go to the movies. Sixteen college students are selected at random from a city and asked how many movies they have seen in theater in the previous year. The data are as follows: 7, 13, 0, 10, 2, 8, 4, 11, 0, 5, 16, 6, 2, 12, 9, 0. Suppose that the national average for movie visits per person in a year is 9.0 and standard deviation is 4.0. a. State the NULL and Alternative hypothesis.b. Test statistically whether college students' habit of watching movie in theatre is significantly different from the population? The 95% region of acceptance for the test-statistic is [-1.96 : 1.96].
Solution
a. The NULL hypothesis is that the average number of movies college students watch in theaters is equal to the national average of 9.0. The Alternative hypothesis is that the average number of movies college students watch in theaters is significantly different from the national average.
b. To test whether college students' movie-watching habits are significantly different from the population, we can use a one-sample t-test. The test statistic is calculated by subtracting the population mean (9.0) from the sample mean and dividing it by the standard deviation (4.0) divided by the square root of the sample size (16).
The calculated test statistic is then compared to the critical values of -1.96 and 1.96, which represent the 95% region of acceptance. If the calculated test statistic falls outside this range, we reject the NULL hypothesis and conclude that the college students' movie-watching habits are significantly different from the population.
To perform the calculation, we first calculate the sample mean of the data provided: (7+13+0+10+2+8+4+11+0+5+16+6+2+12+9+0) / 16 = 6.375.
Next, we calculate the test statistic: (6.375 - 9.0) / (4.0 / sqrt(16)) = -2.625.
Since -2.625 falls outside the range of -1.96 to 1.96, we can reject the NULL hypothesis and conclude that the college students' movie-watching habits are significantly different from the population.
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