Null Hypothesis and Alternative Hypothesis

The given study was conducted to compare the performance of athletes of two States in Inter-State Athlete Meets. Details of the number of successes achieved by the athletes of the two States are given here under:

Does the above information ensure at $1\%$ level of significance that the difference between the performances of the athletes of the two States is significant and mention the null and alternative hypothesis.

The given study was conducted among randomly selected families who are living in two locations of a district, and parents were asked “Whether watching TV program's by parents affects the studies of their children?” Details are presented here under:

Test whether at $5\%$ level of significance, whether the difference between the proportions of families in the two localities agreed the statement and mention the null hypothesis and alternative hypothesis.

The given one thousand apples kept under one type of storage were found to show rotting to the extent of $4\%$ and $1500$ apples kept under another kind of storage showed $3\%$rotting. Can it be reasonably concluded at $5\%$Level of significance that the second type of storage is superior to the first and state the null hypothesis and alternative hypothesis.

Test whether the preference of school students, who participate in Sports events, to do physical exercises in Modern Gymnasium rather than doing aerobic exercises was analyzed. The number of students randomly selected from two States and their preference for Modern Gymnasium are given below.

Whether the difference between proportions of school students who prefer Modern Gymnasium to do their exercises in the two States at the $5\%$ level of significance and state the null hypothesis and alternative hypothesis.

For the given interest of XII Students on Residential Schooling was investigated among randomly selected students from two regions. Among $300$ Students selected from Region A, $34$ Students expressed their interest. Among $200$ Students selected from Region B, $28$ Students expressed their interest. Does this information provide sufficient evidence to conclude at $5\%$ Level of significance that students in Region A are more interested in Residential Schooling than the students in Region B? Find the null hypoyhesis and alternative hypothesis.

For the test of hypotheses for equality of means of two populations when population variance is unknown, calculate the value of the test statistic for the given data sample sizes $m=100,n=150$, sample mean $\overline{x}=50,\overline{y}=51$, sample standard deviation $s_x=4,s_y=5$.

For the test of hypotheses for population mean when population variance is unknown, calculate the value of the test statistic for the given data sample size $n=100$, sample mean $\overline{x}=50$, sample standard deviation $s=5$ and mean of the population is $\mu =35$.

For the test of hypotheses for population mean when population variance is unknown, calculate the value of the test statistic for the given data sample size $n=100$, sample mean $\overline{x}=30$, sample standard deviation $s=3$ and mean of the population is $\mu =27$.

State null hypothesis in general procedure to be followed for testing of hypotheses.

What is meant by critical value in general procedure for testing of hypotheses.

List the general procedure to be followed for testing of hypotheses.

Define type I error and type II error.

Difference between null hypothesis and alternative hypothesis in statistical hypothesis testing.

Discuss in detail about the hypotheses used in one-way ANOVA.

Define: degrees of freedom.

If ${\mu }_{}$ denotes the population mean, then find the critical value to be used for testing $H_0:\mu =100$ against $H_1:\mu <100$ based on $250$ observations at $5\%$ level of significance.

 Formulate the null and alternative hypotheses for testing whether the average time required to $XI$ standard students to complete a Chemistry laboratory exercise is less than $30 \text{minutes}$

Which type of test should be used for testing $H_0:\mu =27$ against $H_1:\mu >27$.

 For testing a null hypothesis against a two-sided alternative hypothesis, if$\left|z_0\right| >z_{\frac{\text{α}}{2}}$ is found to hold, what will be your decision?

Distinguish between null hypothesis and alternative hypothesis.